BUG: Regression in `assert_frame_equal` when using `check_like`
- [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, a copy-pastable example

In `1.2.1`:

```python
>>> import pandas as pd
>>> one = pd.Index([], dtype='object')
>>> two = pd.RangeIndex(start=0, stop=0, step=1)
>>> df_one = pd.DataFrame(index=one)
>>> df_two = pd.DataFrame(index=two)
>>> pd.testing.assert_frame_equal(df_one, df_two, check_like=True)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/nvme/0/pgali/envs/cudfdev/lib/python3.7/site-packages/pandas/_testing.py", line 1655, in assert_frame_equal
    obj=f"{obj}.index",
  File "/nvme/0/pgali/envs/cudfdev/lib/python3.7/site-packages/pandas/_testing.py", line 773, in assert_index_equal
    _check_types(left, right, obj=obj)
  File "/nvme/0/pgali/envs/cudfdev/lib/python3.7/site-packages/pandas/_testing.py", line 740, in _check_types
    assert_class_equal(left, right, exact=exact, obj=obj)
  File "/nvme/0/pgali/envs/cudfdev/lib/python3.7/site-packages/pandas/_testing.py", line 868, in assert_class_equal
    raise_assert_detail(obj, msg, repr_class(left), repr_class(right))
  File "/nvme/0/pgali/envs/cudfdev/lib/python3.7/site-packages/pandas/_testing.py", line 1073, in raise_assert_detail
    raise AssertionError(msg)
AssertionError: DataFrame.index are different

DataFrame.index classes are not equivalent
[left]:  Index([], dtype='object')
[right]: RangeIndex(start=0, stop=0, step=1)
```

In `1.1.5`:

```python
>>> import pandas as pd
>>> one = pd.Index([], dtype='object')
>>> two = pd.RangeIndex(start=0, stop=0, step=1)
>>> df_one = pd.DataFrame(index=one)
>>> df_two = pd.DataFrame(index=two)
>>> pd.testing.assert_frame_equal(df_one, df_two, check_like=True)
```

#### Problem description

Upto `1.1.5`, both `df_one` and `df_two` were considered to be same dataframe when `check_like=True`, but in latest pandas this is broken.

#### Expected Output

```
>>> pd.testing.assert_frame_equal(df_one, df_two, check_like=True)
```

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

<details>


INSTALLED VERSIONS
------------------
commit           : 9d598a5e1eee26df95b3910e3f2934890d062caa
python           : 3.7.9.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.15.0-76-generic
Version          : #86-Ubuntu SMP Fri Jan 17 17:24:28 UTC 2020
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.2.1
numpy            : 1.19.5
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.0.1
setuptools       : 49.6.0.post20210108
Cython           : 0.29.21
pytest           : 6.2.2
hypothesis       : 6.1.1
sphinx           : 3.4.3
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.3
IPython          : 7.20.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : 0.8.5
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 1.0.1
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : 0.52.0

</details>
