BUG: assert_frame_equal() with check_like=True errors with non-comparable types
- [x] I have checked that this issue has not already been reported.
- [x] I have confirmed this bug exists on the latest version of pandas.
- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

#### Code sample

```python
import pandas as pd
import pandas.testing as pdt

# Note that df.columns contains both str and int
df = pd.DataFrame([[0, 1, 2]], columns=["foo", "bar", 42])

pdt.asset_frame_equal(df, df, check_like=True)

```

#### Problem description

This code raises:
```
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-10-05cc1ba40d40> in <module>
----> 1 pdt.assert_frame_equal(df, df, check_like=True)

    [... skipping hidden 2 frame]

~/.local/lib/python3.8/site-packages/pandas/core/indexes/base.py in sort_values(self, return_indexer, ascending, na_position, key)
   4664         # ignore na_position for MultiIndex
   4665         if not isinstance(self, ABCMultiIndex):
-> 4666             _as = nargsort(
   4667                 items=idx, ascending=ascending, na_position=na_position, key=key
   4668             )

~/.local/lib/python3.8/site-packages/pandas/core/sorting.py in nargsort(items, kind, ascending, na_position, key, mask)
    365
    366     if is_extension_array_dtype(items):
--> 367         return items.argsort(ascending=ascending, kind=kind, na_position=na_position)
    368     else:
    369         items = np.asanyarray(items)

~/.local/lib/python3.8/site-packages/pandas/core/arrays/base.py in argsort(self, ascending, kind, na_position, *args, **kwargs)
    584
    585         values = self._values_for_argsort()
--> 586         return nargsort(
    587             values,
    588             kind=kind,

~/.local/lib/python3.8/site-packages/pandas/core/sorting.py in nargsort(items, kind, ascending, na_position, key, mask)
    377         non_nans = non_nans[::-1]
    378         non_nan_idx = non_nan_idx[::-1]
--> 379     indexer = non_nan_idx[non_nans.argsort(kind=kind)]
    380     if not ascending:
    381         indexer = indexer[::-1]

TypeError: '<' not supported between instances of 'int' and 'str'
```

The cause is PR #37479, which added the following to `assert_index_equal()`:
```python
    # If order doesn't matter then sort the index entries
    if not check_order:
        left = left.sort_values()
        right = right.sort_values()
```
This is code is triggered by `assert_frame_equal(…, check_like=True)`. `.sort_order()` does not work when an index contains non-comparable types, like `str` and `int`.

Detected via iiasa/ixmp#390.

#### Expected output

In pandas < 1.2.0, the last line above returned `True`.

The description of the `check_like` argument is:
https://github.com/pandas-dev/pandas/blob/25110a92b291de6688c3accad4c34d84837445e8/pandas/_testing/asserters.py#L1127-L1130
…i.e. this does not indicate that the columns index may only contain comparable types, so the function should not raise an exception.


#### Output of ``pd.show_versions()``

<details>


INSTALLED VERSIONS
------------------
commit           : 3e89b4c4b1580aa890023fc550774e63d499da25
python           : 3.8.6.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.8.0-36-generic
Version          : #40-Ubuntu SMP Tue Jan 5 21:54:35 UTC 2021
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_CA.UTF-8
LOCALE           : en_CA.UTF-8

pandas           : 1.2.0
numpy            : 1.19.4
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.3.3
setuptools       : 50.3.2
Cython           : 0.29.21
pytest           : 6.1.2
hypothesis       : None
sphinx           : 3.3.0
blosc            : 1.8.1
feather          : None
xlsxwriter       : 1.3.7
lxml.etree       : 4.5.2
html5lib         : 1.1
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.19.0
pandas_datareader: None
bs4              : 4.9.1
bottleneck       : 1.3.2
fsspec           : 0.6.1
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.3
numexpr          : 2.7.1
odfpy            : None
openpyxl         : 3.0.5
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.4
sqlalchemy       : 1.3.19
tables           : 3.6.1
tabulate         : 0.8.6
xarray           : 0.16.1
xlrd             : 1.2.0
xlwt             : 1.3.0
numba            : 0.51.2

</details>
