"The owner of the practice thinks all of this is overblown and it's business as usual. I have literally never seen him wash his hands before touching anything, even when he has a cold, so the spread of germs is highly likely."

Then nothing is a problem for him. You, on the other hand, need to take control for your own sake, for your own risk. Don't expect to change the office environment when the supposed Leader should be doing so.

I saw a good comment: Why is all of this hand washing and other protective guidance considered New? You were supposed to be doing things like this all along.