OTB rule question

Hello, I just have a quick question. Is it allowed to touch the physical board while playing chess?

Yes

So, like, even if it is an unreasonable amount, like tapping each square during your turn, like one of my annoying OTB chess club opponents did?

No that is not allowed. Now if you're playing and you're blind or visually impaired then yes you can touch the board. We had a couple online speed chess ayers show up at the club and thought they were still playing online. Being annoying, slamming down the pieces and touching all the squares. They don't come back anymore.

If you play tournament game, just call the arbiter. If you are playing casual game, just tell the opponent politely to stop doing it. If he doesn’t stop doing it you stop playing him.

Tapping the board persistently would most likely be considered a form of annoyance or distraction, which is explicitly prohibited in formal (tournament) play.