I can tie anything that comes my way with some practice.

In that case, you're probably well ahead of the game.

Loud noises: people calling instructions to belayers, occasionally thumps as boulderers hit the mats. I'm very noise-sensitive, and for me, it only gets problematic if there's a school party in.

There might be skin contact in passing to get a harness adjusted or demonstrate how to tie a knot. If someone freaks out completely on the bouldering wall and doesn't feel able to get down, an instructor might climb up next to them and offer them a hand. Otherwise, no, I wouldn't expect touching.

(FWIW, it sounds like we have some fairly similar sensory issues, so if I found it tolerable in those respects, you probably will.)