BUG: Do not use string Index like Datetimelike Index
Follow up of conversation in https://github.com/pandas-dev/pandas/pull/32739#issuecomment-602271577.

The goal is to prevent index of string that look like datetimelike to be used as datetimelike.

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