Re: concerns about sitting on public toilets without using one of those paper shield thingies (which I don’t), the one seriously transmissible potential problem is pinworm.
Had a roommate who picked it up at his workplace, and had to take a month’s worth of pills that turned his poop the most vivid yellow. (According to him — blessedly I never caught sight thereof.)
And to protect the rest of us living there, he had to disinfect the seat with Lysol after every use.
So caveat sedenti!