BUG: assert_frame_equal still checks category dtypes even when asked not to check index type

[caneff]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import numpy as np
import pandas as pd
df = pd.DataFrame({"x": [1, 2]})
df.index = pd.MultiIndex.from_arrays(
    [pd.Categorical(np.array([1, 2], dtype=np.uint64))]
)
df2.index = pd.MultiIndex.from_arrays(
    [pd.Categorical(np.array([1, 2], dtype=np.int64))]
)
pd.testing.assert_frame_equal(df, df2, check_categorical=False, check_index_type=False)

Issue Description

When testing two indices and I ask to not check index type I don't think it should check the type of categories of the of type of an index level either.

Note that for a normal index things behave better:

df = pd.DataFrame({"x": [1, 2]})
df.index = pd.Index(pd.Categorical(np.array([1, 2], dtype=np.int64)))
df2.index = pd.Index(pd.Categorical(np.array([1, 2], dtype=np.uint64)))
pd.testing.assert_frame_equal(df, df2, check_categorical=False)

Passes as I'd expect.

Expected Behavior

df = pd.DataFrame({"x": [1, 2]})
df.index = pd.MultiIndex.from_arrays(
    [pd.Categorical(np.array([1, 2], dtype=np.uint64))]
)
df2.index = pd.MultiIndex.from_arrays(
    [pd.Categorical(np.array([1, 2], dtype=np.int64))]
)
pd.testing.assert_frame_equal(df, df2, check_categorical=False, check_index_type=False)

Expected behavior: passes. Nothing is printed.

Actual behavior:

AssertionError                            Traceback (most recent call last)
Cell In[163], line 8
      2 df.index = pd.MultiIndex.from_arrays(
      3     [pd.Categorical(np.array([1, 2], dtype=np.uint64))]
      4 )
      5 df2.index = pd.MultiIndex.from_arrays(
      6     [pd.Categorical(np.array([1, 2], dtype=np.int64))]
      7 )
----> 8 pd.testing.assert_frame_equal(df, df2, check_categorical=False, check_index_type=False)

    [... skipping hidden 3 frame]

File ~/.local/lib/python3.10/site-packages/pandas/_testing/asserters.py:479, in assert_categorical_equal(left, right, check_dtype, check_category_order, obj)
    476     exact = True
    478 if check_category_order:
--> 479     assert_index_equal(
    480         left.categories, right.categories, obj=f"{obj}.categories", exact=exact
    481     )
    482     assert_numpy_array_equal(
    483         left.codes, right.codes, check_dtype=check_dtype, obj=f"{obj}.codes"
    484     )
    485 else:

    [... skipping hidden 1 frame]

File ~/.local/lib/python3.10/site-packages/pandas/_testing/asserters.py:247, in assert_index_equal.<locals>._check_types(left, right, obj)
    244         assert_index_equal(left.categories, right.categories, exact=exact)
    245     return
--> 247 assert_attr_equal("dtype", left, right, obj=obj)

    [... skipping hidden 1 frame]

File ~/.local/lib/python3.10/site-packages/pandas/_testing/asserters.py:595, in raise_assert_detail(obj, message, left, right, diff, first_diff, index_values)
    592 if first_diff is not None:
    593     msg += f"\n{first_diff}"
--> 595 raise AssertionError(msg)

AssertionError: MultiIndex level [0] category.categories are different

Attribute "dtype" are different
[left]:  uint64
[right]: int64

Installed Versions

INSTALLED VERSIONS

commit : 5c15588
python : 3.10.9.final.0
python-bits : 64
OS : Linux
OS-release : 5.19.11-1rodete1-amd64
Version : #1 SMP PREEMPT_DYNAMIC Debian 5.19.11-1rodete1 (2022-10-31)
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.0.dev0+284.g5c155883fd
numpy : 1.21.5
pytz : 2022.6
dateutil : 2.8.2
setuptools : 65.6.3
pip : 22.3.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.9.1
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.10.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : None
brotli : 1.0.9
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : 1.2.0
zstandard : None
tzdata : 2022.7
qtpy : None
pyqt5 : None

[DeaMariaLeon]

Thanks for the report @caneff
I was able to reproduce the bug, but df2 is not defined on your example.