But what about people who don't fancy being touched, either because of principle or earlier trauma? Are they disqualified to work in psychiatry?
I'm going to go with "yes". That's like being a surgeon who's traumatised by the sight of blood.
Not really. Every surgeon will be dealing with blood, while not every psychiatrist is going to engage with people who do the whole “sexual inappropriateness” dealio.
Psychiatrists generally also have counseling available to them, given what they have to deal with.
Further, someone with a fear of blood will likely be turned off from a medical career anyway, while someone who has experienced trauma may want to help other people deal with it in the future.