Init arguments upon multiple inheritance from LightningDataModule and other parent class

Bug description

When defining a new class inheriting from both lightning.pytorch.LightningDataModule and a user-defined parent class, a TypeError is raised upon initialization of an instance of the new class.

Expected behavior: no TypeError when inheriting from lightning.pytorch.LightningDataModule (see Check2 in the MRE) and docs.

What version are you seeing the problem on?

2.0+

How to reproduce the bug

from lightning.pytorch import LightningDataModule

class Base:
    def __init__(self, foo):
        print(foo)

class Other:
    def __init__(self):
        pass

class Check1(Other, Base):
    def __init__(self, config):
        Other.__init__(self)
        Base.__init__(self, **config)

class Check2(LightningDataModule):
    def __init__(self):
        LightningDataModule.__init__(self)

class CustomDataModule(LightningDataModule, Base):
    def __init__(self, config):
        LightningDataModule.__init__(self)
        Base.__init__(self, **config)


if __name__ == "__main__":
    config = {"foo": "foo"}
    Check1(config)
    Check2()
    CustomDataModule(config)

Error messages and logs

Traceback (most recent call last):
  File ".../debug.py", line 35, in <module>
    CustomDataModule(config)
  File ".../debug.py", line 27, in __init__
    LightningDataModule.__init__(self)
  File ".../.pyenv/versions/3.8.10/envs/frm_test/lib/python3.8/site-packages/lightning/pytorch/core/datamodule.py", line 64, in __init__
    super().__init__()
  File .../.pyenv/versions/3.8.10/envs/frm_test/lib/python3.8/site-packages/lightning/pytorch/core/hooks.py", line 298, in __init__
    super().__init__()
  File ".../.pyenv/versions/3.8.10/envs/frm_test/lib/python3.8/site-packages/lightning/pytorch/core/mixins/hparams_mixin.py", line 31, in __init__
    super().__init__()
TypeError: __init__() missing 1 required positional argument: 'foo'

Environment

* CUDA:
        - GPU:               None
        - available:         False
        - version:           11.7
* Lightning:
        - lightning:         2.0.1.post0
        - lightning-cloud:   0.5.32
        - lightning-utilities: 0.8.0
        - pytorch-lightning: 2.0.0
        - torch:             2.0.0
        - torch-tb-profiler: 0.4.1
        - torchmetrics:      0.11.4
        - torchsummary:      1.5.1
        - torchview:         0.2.6
        - torchvision:       0.15.1
* Packages:
        - absl-py:           1.4.0
        - affine:            2.4.0
        - aiofiles:          22.1.0
        - aiohttp:           3.8.4
        - aiosignal:         1.3.1
        - aiosqlite:         0.18.0
        - alembic:           1.9.2
        - anyio:             3.6.2
        - argon2-cffi:       21.3.0
        - argon2-cffi-bindings: 21.2.0
        - arrow:             1.2.3
        - asciitree:         0.3.3
        - asttokens:         2.0.8
        - astunparse:        1.6.3
        - async-timeout:     4.0.2
        - attrs:             22.1.0
        - autopage:          0.5.1
        - babel:             2.10.3
        - backcall:          0.2.0
        - backoff:           2.2.1
        - beautifulsoup4:    4.11.1
        - bleach:            5.0.1
        - blessed:           1.20.0
        - bokeh:             2.4.3
        - bottle:            0.12.25
        - bqplot:            0.12.36
        - branca:            0.5.0
        - cachetools:        5.2.0
        - certifi:           2022.9.24
        - cffi:              1.15.1
        - cftime:            1.6.2
        - charset-normalizer: 2.1.1
        - click:             8.1.3
        - click-plugins:     1.1.1
        - cliff:             4.2.0
        - cligj:             0.7.2
        - cloudpickle:       2.2.1
        - cmaes:             0.9.1
        - cmake:             3.26.0
        - cmd2:              2.4.3
        - colorlog:          6.7.0
        - colour:            0.1.5
        - comm:              0.1.2
        - compress-json:     1.0.8
        - contourpy:         1.0.5
        - croniter:          1.3.8
        - cycler:            0.11.0
        - dask:              2022.12.0
        - dask-optuna:       0.0.2
        - dateutils:         0.6.12
        - debugpy:           1.6.3
        - decorator:         5.1.1
        - deepdiff:          6.3.0
        - defusedxml:        0.7.1
        - dill:              0.3.6
        - distributed:       2022.12.0
        - dnspython:         2.3.0
        - docopt:            0.6.2
        - earthengine-api:   0.1.343
        - ee-extra:          0.0.14
        - eerepr:            0.0.4
        - email-validator:   1.3.1
        - entrypoints:       0.4
        - executing:         1.1.1
        - fastapi:           0.88.0
        - fasteners:         0.18
        - fastjsonschema:    2.16.2
        - ffmpeg-python:     0.2.0
        - filelock:          3.8.0
        - fiona:             1.8.22
        - flask:             2.2.2
        - flatbuffers:       23.1.21
        - folium:            0.13.0
        - fonttools:         4.38.0
        - fqdn:              1.5.1
        - frarssmap:         0.0.0
        - frozenlist:        1.3.3
        - fsspec:            2023.1.0
        - future:            0.18.2
        - gast:              0.4.0
        - gdown:             4.5.3
        - geeadd:            0.5.6
        - geemap:            0.17.1
        - geocoder:          1.38.1
        - geojson:           2.5.0
        - geopandas:         0.10.2
        - google-api-core:   2.10.2
        - google-api-python-client: 1.12.11
        - google-auth:       2.17.2
        - google-auth-httplib2: 0.1.0
        - google-auth-oauthlib: 0.4.6
        - google-cloud-core: 2.3.2
        - google-cloud-storage: 2.5.0
        - google-crc32c:     1.5.0
        - google-pasta:      0.2.0
        - google-resumable-media: 2.4.0
        - googleapis-common-protos: 1.56.4
        - greenlet:          2.0.2
        - grip:              4.6.1
        - grpcio:            1.51.1
        - h11:               0.14.0
        - h3:                3.7.4
        - h3pandas:          0.2.3
        - h5py:              3.8.0
        - heapdict:          1.0.1
        - httpcore:          0.16.3
        - httplib2:          0.20.4
        - httplib2shim:      0.0.3
        - httptools:         0.5.0
        - httpx:             0.23.3
        - idna:              3.4
        - importlib-metadata: 5.0.0
        - importlib-resources: 5.10.0
        - inquirer:          3.1.3
        - ipyevents:         2.0.1
        - ipyfilechooser:    0.6.0
        - ipykernel:         6.16.2
        - ipyleaflet:        0.17.2
        - ipython:           8.5.0
        - ipython-genutils:  0.2.0
        - ipytree:           0.2.2
        - ipywidgets:        7.6.5
        - isoduration:       20.11.0
        - itsdangerous:      2.1.2
        - jedi:              0.18.1
        - jinja2:            3.1.2
        - joblib:            1.2.0
        - json5:             0.9.10
        - jsonpointer:       2.3
        - jsonschema:        4.16.0
        - jupyter:           1.0.0
        - jupyter-client:    7.1.0
        - jupyter-console:   6.4.4
        - jupyter-contrib-core: 0.4.2
        - jupyter-contrib-nbextensions: 0.5.1
        - jupyter-core:      4.9.1
        - jupyter-events:    0.5.0
        - jupyter-highlight-selected-word: 0.2.0
        - jupyter-latex-envs: 1.4.6
        - jupyter-nbextensions-configurator: 0.6.1
        - jupyter-server:    1.13.1
        - jupyter-server-fileid: 0.6.0
        - jupyter-server-terminals: 0.4.4
        - jupyter-server-ydoc: 0.6.1
        - jupyter-ydoc:      0.2.2
        - jupyterlab:        3.2.5
        - jupyterlab-pygments: 0.1.2
        - jupyterlab-server: 2.10.2
        - jupyterlab-sublime: 0.4.1
        - jupyterlab-widgets: 1.0.2
        - kaleido:           0.2.1
        - keras:             2.11.0
        - kiwisolver:        1.4.4
        - libclang:          15.0.6.1
        - lightgbm:          3.3.5
        - lightning:         2.0.1.post0
        - lightning-cloud:   0.5.32
        - lightning-utilities: 0.8.0
        - lit:               16.0.0
        - locket:            1.0.0
        - logzero:           1.7.0
        - lxml:              4.9.2
        - mako:              1.2.4
        - markdown:          3.4.1
        - markdown-it-py:    2.2.0
        - markupsafe:        2.1.1
        - matplotlib:        3.6.3
        - matplotlib-inline: 0.1.6
        - mdurl:             0.1.2
        - mistune:           0.8.4
        - mpmath:            1.3.0
        - msgpack:           1.0.4
        - multidict:         6.0.4
        - multiprocess:      0.70.14
        - munch:             2.5.0
        - nbclassic:         0.3.4
        - nbclient:          0.5.9
        - nbconvert:         6.4.0
        - nbformat:          5.1.3
        - nest-asyncio:      1.5.6
        - netcdf4:           1.6.2
        - netron:            6.5.5
        - networkx:          3.0
        - notebook:          6.1.5
        - notebook-shim:     0.2.0
        - numcodecs:         0.11.0
        - numpy:             1.23.4
        - nvidia-cublas-cu11: 11.10.3.66
        - nvidia-cuda-cupti-cu11: 11.7.101
        - nvidia-cuda-nvrtc-cu11: 11.7.99
        - nvidia-cuda-runtime-cu11: 11.7.99
        - nvidia-cudnn-cu11: 8.5.0.96
        - nvidia-cufft-cu11: 10.9.0.58
        - nvidia-curand-cu11: 10.2.10.91
        - nvidia-cusolver-cu11: 11.4.0.1
        - nvidia-cusparse-cu11: 11.7.4.91
        - nvidia-nccl-cu11:  2.14.3
        - nvidia-nvtx-cu11:  11.7.91
        - oauthlib:          3.2.2
        - opt-einsum:        3.3.0
        - optuna:            3.1.0
        - optuna-dashboard:  0.9.0
        - ordered-set:       4.1.0
        - orjson:            3.8.8
        - packaging:         21.3
        - pandas:            1.5.1
        - pandocfilters:     1.5.0
        - parso:             0.8.3
        - partd:             1.3.0
        - path-and-address:  2.0.1
        - pathos:            0.3.0
        - pbr:               5.11.1
        - pexpect:           4.8.0
        - pickleshare:       0.7.5
        - pillow:            9.2.0
        - pip:               21.1.1
        - pipreqs:           0.4.11
        - pkgutil-resolve-name: 1.3.10
        - platformdirs:      2.6.2
        - plot-keras-history: 1.1.38
        - plotly:            5.13.1
        - pox:               0.3.2
        - ppft:              1.7.6.6
        - prettytable:       3.6.0
        - prometheus-client: 0.15.0
        - prompt-toolkit:    3.0.31
        - protobuf:          3.19.6
        - psutil:            5.9.3
        - ptyprocess:        0.7.0
        - pure-eval:         0.2.2
        - py:                1.11.0
        - pyarrow:           6.0.1
        - pyasn1:            0.4.8
        - pyasn1-modules:    0.2.8
        - pycparser:         2.21
        - pycrs:             1.0.2
        - pydantic:          1.10.7
        - pygments:          2.13.0
        - pyjwt:             2.6.0
        - pyparsing:         3.0.9
        - pyperclip:         1.8.2
        - pyproj:            3.4.0
        - pyrsistent:        0.18.1
        - pyshp:             2.3.1
        - pysocks:           1.7.1
        - python-box:        6.0.2
        - python-dateutil:   2.8.2
        - python-dotenv:     1.0.0
        - python-editor:     1.0.4
        - python-json-logger: 2.0.4
        - python-multipart:  0.0.6
        - pytorch-lightning: 2.0.0
        - pytz:              2022.5
        - pyyaml:            6.0
        - pyzmq:             24.0.1
        - qtconsole:         5.4.0
        - qtpy:              2.3.0
        - rasterio:          1.3.5
        - ratelim:           0.1.6
        - readchar:          4.0.5
        - requests:          2.28.1
        - requests-oauthlib: 1.3.1
        - requests-toolbelt: 0.10.1
        - restee:            0.0.3
        - retry:             0.9.2
        - retrying:          1.3.3
        - rfc3339-validator: 0.1.4
        - rfc3986:           1.5.0
        - rfc3986-validator: 0.1.1
        - rich:              13.3.3
        - rsa:               4.9
        - ruamel.yaml:       0.17.21
        - ruamel.yaml.clib:  0.2.7
        - sanitize-ml-labels: 1.0.50
        - sankee:            0.2.0
        - scikeras:          0.10.0
        - scikit-learn:      1.1.3
        - scipy:             1.9.3
        - scooby:            0.7.0
        - seaborn:           0.12.2
        - send2trash:        1.8.0
        - setuptools:        56.0.0
        - shapely:           1.8.5.post1
        - six:               1.16.0
        - sklearn-pandas:    2.2.0
        - sniffio:           1.3.0
        - snuggs:            1.4.7
        - sortedcontainers:  2.4.0
        - soupsieve:         2.3.2.post1
        - sqlalchemy:        2.0.2
        - stack-data:        0.5.1
        - starlette:         0.22.0
        - starsessions:      1.3.0
        - stevedore:         5.0.0
        - support-developer: 1.0.5
        - sympy:             1.11.1
        - tb-nightly:        2.13.0a20230412
        - tblib:             1.7.0
        - tenacity:          8.1.0
        - tensorboard:       2.11.2
        - tensorboard-data-server: 0.6.1
        - tensorboard-plugin-wit: 1.8.1
        - tensorflow:        2.11.0
        - tensorflow-estimator: 2.11.0
        - tensorflow-io-gcs-filesystem: 0.28.0
        - termcolor:         2.0.1
        - terminado:         0.17.0
        - testpath:          0.6.0
        - threadpoolctl:     3.1.0
        - tinycss2:          1.2.1
        - tomli:             2.0.1
        - toolz:             0.12.0
        - torch:             2.0.0
        - torch-tb-profiler: 0.4.1
        - torchmetrics:      0.11.4
        - torchsummary:      1.5.1
        - torchview:         0.2.6
        - torchvision:       0.15.1
        - tornado:           6.2
        - tqdm:              4.64.1
        - traitlets:         5.5.0
        - traittypes:        0.2.1
        - triton:            2.0.0
        - typing-extensions: 4.4.0
        - ujson:             5.7.0
        - uri-template:      1.2.0
        - uritemplate:       3.0.1
        - urllib3:           1.26.12
        - uvicorn:           0.21.1
        - uvloop:            0.17.0
        - watchfiles:        0.19.0
        - wcwidth:           0.2.5
        - webcolors:         1.12
        - webencodings:      0.5.1
        - websocket-client:  1.4.1
        - websockets:        10.4
        - werkzeug:          2.2.2
        - wheel:             0.38.4
        - whitebox:          2.2.0
        - whiteboxgui:       2.2.0
        - widgetsnbextension: 3.5.2
        - wrapt:             1.14.1
        - wxee:              0.3.3
        - xarray:            2022.11.0
        - xgboost:           1.7.5
        - xyzservices:       2022.9.0
        - y-py:              0.5.5
        - yarg:              0.1.9
        - yarl:              1.8.2
        - ypy-websocket:     0.8.2
        - zarr:              2.10.3
        - zict:              2.2.0
        - zipp:              3.10.0
* System:
        - OS:                Linux
        - architecture:
                - 64bit
                - ELF
        - processor:         x86_64
        - python:            3.8.10
        - version:           #1 SMP Fri Jan 27 02:56:13 UTC 2023

More info

No response

cc @carmocca @awaelchli @borda