BUG: idxmax and idxmin do not allow string columns when numeric_only=False

[mvashishtha]

Modin version checks

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

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

• I have confirmed this bug exists on the main branch of Modin. (In order to do this you can follow this guide.)

Reproducible Example

import modin.pandas as pd

df = pd.DataFrame([['a', 'b']])
df.idxmax(axis=0)
df.idxmax(axis=1)
df.idxmin(axis=0)
df.idxmin(axis=1)

Issue Description

Need to only check the types if numeric_only here and here.

Expected Behavior

like in pandas, idxmax and idxmin should allow string columns in both dimensions.

Error Logs

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[6], line 1
----> 1 df.idxmin(axis=1)

File ~/sources/modin/modin/logging/logger_decorator.py:125, in enable_logging.<locals>.decorator.<locals>.run_and_log(*args, **kwargs)
    110 """
    111 Compute function with logging if Modin logging is enabled.
    112
   (...)
    122 Any
    123 """
    124 if LogMode.get() == "disable":
--> 125     return obj(*args, **kwargs)
    127 logger = get_logger()
    128 logger.log(log_level, start_line)

File ~/sources/modin/modin/pandas/base.py:1882, in BasePandasDataset.idxmin(self, axis, skipna, numeric_only)
   1878 """
   1879 Return index of first occurrence of minimum over requested axis.
   1880 """
   1881 if not all(d != np.dtype("O") for d in self._get_dtypes()):
-> 1882     raise TypeError("reduce operation 'argmin' not allowed for this dtype")
   1883 axis = self._get_axis_number(axis)
   1884 return self._reduce_dimension(
   1885     self._query_compiler.idxmin(
   1886         axis=axis, skipna=skipna, numeric_only=numeric_only
   1887     )
   1888 )

TypeError: reduce operation 'argmin' not allowed for this dtype

Installed Versions

UserWarning: Setuptools is replacing distutils.

INSTALLED VERSIONS
------------------
commit                : c75343687799e3b69fc04a99b8a9d11eab1fd984
python                : 3.9.18.final.0
python-bits           : 64
OS                    : Darwin
OS-release            : 23.4.0
Version               : Darwin Kernel Version 23.4.0: Wed Feb 21 21:45:49 PST 2024; root:xnu-10063.101.15~2/RELEASE_ARM64_T6020
machine               : arm64
processor             : arm
byteorder             : little
LC_ALL                : None
LANG                  : en_US.UTF-8
LOCALE                : en_US.UTF-8

Modin dependencies
------------------
modin                 : 0.28.0+23.gc7534368
ray                   : 2.8.0
dask                  : None
distributed           : None
hdk                   : None

pandas dependencies
-------------------
pandas                : 2.2.1
numpy                 : 1.26.1
pytz                  : 2023.3.post1
dateutil              : 2.8.2
setuptools            : 68.0.0
pip                   : 23.3
Cython                : None
pytest                : None
hypothesis            : None
sphinx                : None
blosc                 : None
feather               : None
xlsxwriter            : None
lxml.etree            : None
html5lib              : None
pymysql               : None
psycopg2              : None
jinja2                : 3.1.2
IPython               : 8.17.2
pandas_datareader     : None
adbc-driver-postgresql: None
adbc-driver-sqlite    : None
bs4                   : None
bottleneck            : None
dataframe-api-compat  : None
fastparquet           : None
fsspec                : 2023.10.0
gcsfs                 : None
matplotlib            : 3.8.1
numba                 : None
numexpr               : None
odfpy                 : None
openpyxl              : None
pandas_gbq            : None
pyarrow               : 14.0.1
pyreadstat            : None
python-calamine       : None
pyxlsb                : None
s3fs                  : None
scipy                 : 1.11.3
sqlalchemy            : None
tables                : None
tabulate              : None
xarray                : None
xlrd                  : None
zstandard             : None
tzdata                : 2023.3
qtpy                  : None
pyqt5                 : None