Like everything you get used to it. I know I'm not a medic but watching things like oral surgery can make me squeamish whereas doing it is no bother. You're too focused. You learn ways to deal with something. If someone/thing smells bad, mask up and say you have a cold and don't want to pass it on. If you feel a bit queazy, disappear for a minute or two and say you're going to get something.
Having said that though, the first time I pulled a tooth I felt queazy for a few minutes.
I was worried about this too but you just tend to deal with it because there's no other option. I've seen mouths worse than the ones on embarrassing bodies and I may cringe for a minute but then I realise, ok, I have work to do. And you would be the same as a medic.
And I believe people go on this to get their treatment paid for?