Hi cherryberrymum, I'm sorry this is stressing you out.
Priests are normal people, just like you and me, and are no more or less likely to be perfect OR sinful than anybody else.
Having said that, you are right, they are 'strangers' to your child, and it's sensible to teach them safe ways of interacting with any adult they don't know - particularly those in positions of authority: teachers, doctors etc.
I think there's also a strong cultural element at play, in that you speak of your Irish up-bringing in which priests were treated as mini-deities. This is a tricky one: priests are fallible human beings like all of us; however, it is true that their role, as distinct from they themselves (Fr. Jack/Andrew/Robbie etc), is worthy of particular respect, because, for Roman Catholics, they represent Jesus Christ. This is why we treat the priestly role with particular respect.
Having said that, I'm sure you teach your children to respect their teachers, not because they're necessarily fabulous human beings, but because they have a particular role of authority in the community. So maybe that might be a helpful way to think about this, in a more general way.