BUG: Fix assert_equal when check_exact=True for non-numeric dtypes #3…
`assert_series_equal(..., check_exact=True)` no longer raises an error when series has a non-numeric dtype. This fixes a bug/ regression introduced in `1.1.0`.

- [x] closes #35446
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

I've added a very simple test, but could add more. For instance, there could be a check on `assert_frame_equal`, but I'm not sure what the desired strategy is for that.

I've left off the `whatsnew` entry for now since I figure that's the most likely to generate conflicts while this gets reviewed.