BUG: assert_series_equal b/w datetime column with equivalent object column fails with check_dtype=False

[VibhuJawa]

• 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 master branch of pandas.

Reproducible Example

import pandas  as pd

s1 = pd.Series(['2020-01-01 00:00:00'])
s2 = pd.to_datetime(s1)
pd.testing.assert_series_equal(s1,s2,check_dtype=False)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/nfs/vjawa/pandas/pandas/_testing/asserters.py", line 1078, in assert_series_equal
    _testing.assert_almost_equal(
  File "pandas/_libs/testing.pyx", line 53, in pandas._libs.testing.assert_almost_equal
    cpdef assert_almost_equal(a, b,
  File "pandas/_libs/testing.pyx", line 168, in pandas._libs.testing.assert_almost_equal
    raise_assert_detail(obj, msg, lobj, robj, index_values=index_values)
  File "/home/nfs/vjawa/pandas/pandas/_testing/asserters.py", line 666, in raise_assert_detail
    raise AssertionError(msg)
AssertionError: Series are different

Series values are different (100.0 %)
[index]: [0]
[left]:  [2020-01-01 00:00:00]
[right]: <DatetimeArray>
['2020-01-01 00:00:00']
Length: 1, dtype: datetime64[ns]

Issue Description

BUG: assert_series_equal b/w datetime column with equivalent object column fails with check_dtype=False

When trying to compare two series where one is an object and the other is an equivalent date-time created using pd.to_datetime , we get a unexpected AssertionError.

Expected Behavior

I would expect that we pass the assertion.

Installed Versions

INSTALLED VERSIONS

commit : 36d5c9b
python : 3.9.7.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 : 1.4.0.dev0+745.g36d5c9b8e5
numpy : 1.20.3
pytz : 2021.1
dateutil : 2.8.2
pip : 21.2.4
setuptools : 58.0.4
Cython : 0.29.24
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : 1.3.2
fsspec : None
fastparquet : None
gcsfs : None
matplotlib : None
numexpr : 2.7.3
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
numba : None

[Xabilahu]

Assertion fails because inner elements have different classes:
type(s1._values[0]) == <class 'str'> vs type(s2._values[0]) = <class 'pandas._libs.tslibs.timestamps.Timestamp'>

>>> pd._testing.assert_class_equal(s1._values[0], s2._values[0])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/xabi/.conda/envs/nlp/lib/python3.9/site-packages/pandas/_testing/asserters.py", line 459, in assert_class_equal
    raise_assert_detail(obj, msg, repr_class(left), repr_class(right))
  File "/home/xabi/.conda/envs/nlp/lib/python3.9/site-packages/pandas/_testing/asserters.py", line 665, in raise_assert_detail
    raise AssertionError(msg)
AssertionError: Input are different

Input classes are different
[left]:  str
[right]: Timestamp

Classes are checked due to isiterable(s1._values[0]) and not isiterable(s2._values[0]) in testing.pyx:119

[jreback]

check_dtype code is not designed to bypass the entire check otherwise what's the point