EHN: Improved thread safety for read_html() GH16928
 - [X] closes #16928
 - [x] tests added / passed
 - [X] passes ``git diff upstream/master --name-only -- '*.py' | flake8 --diff`` (On Windows, ``git diff upstream/master -u -- "*.py" | flake8 --diff`` might work as an alternative.)
 - [X] whatsnew entry

It failed a total of 6 tests when running `test_fast.sh` but failed none when running `pytest pandas/tests/io/test_html.py`.
It seems that these 6 failed tests are unrelated to my changes since they also occur on the master branch.