• [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.

  • [x] (optional) I have confirmed this bug exists on the master branch of pandas.


Note: Please read this guide detailing how to provide the necessary information for us to reproduce your bug.

Code Sample, a copy-pastable example

>>> import pandas as pd
>>> index = pd.MultiIndex.from_tuples([(('a', None), 1), (('b', None), 2)])
>>> index2 = pd.MultiIndex.from_tuples([(('b', None), 2), (('a', None), 1)])
>>> df1_dtype = pd.DataFrame([1,2], index=index)
>>> df2_dtype = pd.DataFrame([2,1], index=index2)
>>> df1_dtype.reindex_like(df2_dtype)
              0
(b, None) 2 NaN
(a, None) 1 NaN
>>> import pandas as pd
>>> import numpy as np
>>> index = pd.MultiIndex.from_tuples([(('a', np.nan), 1), (('b', np.nan), 2)])
>>> index2 = pd.MultiIndex.from_tuples([(('b', np.nan), 2), (('a', np.nan), 1)])
>>> df1_dtype = pd.DataFrame([1,2], index=index)
>>> df2_dtype = pd.DataFrame([2,1], index=index2)
>>> df1_dtype.reindex_like(df2_dtype)
            0
(b, nan) 2  2
(a, nan) 1  1

Problem description

I would expect the two indices to align here.

Expected Output

>>> import pandas as pd
>>> index = pd.MultiIndex.from_tuples([(('a', None), 1), (('b', None), 2)])
>>> index2 = pd.MultiIndex.from_tuples([(('b', None), 2), (('a', None), 1)])
>>> df1_dtype = pd.DataFrame([1,2], index=index)
>>> df2_dtype = pd.DataFrame([2,1], index=index2)
>>> df1_dtype.reindex_like(df2_dtype)
            0
(b, None) 2  2
(a, None) 1  1

Output of pd.show_versions()

>>> pd.show_versions()

INSTALLED VERSIONS
------------------
commit           : 226876a55b82324b92449256bab47d431b22310f
python           : 3.8.5.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.19.128-microsoft-standard
Version          : #1 SMP Tue Jun 23 12:58:10 UTC 2020
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : C.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.4.0.dev0+357.g226876a55b
numpy            : 1.21.1
pytz             : 2021.1
dateutil         : 2.8.2
pip              : 21.2.2
setuptools       : 57.4.0
Cython           : 0.29.24
pytest           : 6.2.4
hypothesis       : 6.14.5
sphinx           : 4.1.2
blosc            : 1.10.4
feather          : None
xlsxwriter       : 1.4.4
lxml.etree       : 4.6.3
html5lib         : 1.1
pymysql          : None
psycopg2         : None
jinja2           : 3.0.1
IPython          : 7.25.0
pandas_datareader: None
bs4              : 4.9.3
bottleneck       : 1.3.2
fsspec           : 2021.05.0
fastparquet      : 0.6.3
gcsfs            : 2021.07.0
matplotlib       : 3.4.2
numexpr          : 2.7.3
odfpy            : None
openpyxl         : 3.0.7
pandas_gbq       : None
pyarrow          : 5.0.0
pyxlsb           : None
s3fs             : None
scipy            : 1.7.0
sqlalchemy       : 1.4.22
tables           : 3.6.1
tabulate         : 0.8.9
xarray           : 0.18.2
xlrd             : 2.0.1
xlwt             : 1.3.0
numba            : 0.53.1