If you have a personal connection to a professor, do write to them and let them know that you will not be accepting. At places where you don’t have the connection, let the college know via the portal - do this even if you have written to the professor. For the most part, professors are gracious - they haven’t gotten where they are without rejecting a few themselves, and they’ve been rejected by others as well. In the worst case, you may never hear from them again, which is OK.
But, do let them know, as soon as possible. There are people on the waitlist that may benefit. This is particularly important for music school I think, since there are potentially two lists, one for a specific professors studio, and the second for the school itself. Letting both know as soon as you can is the right thing to do.
A not necessarily related anecdote : Some years ago, there was a Canadian wind player (?) that had a MM offer from USC. His live in girlfriend was not accepted, and having access to the guys email, deleted it before he could see it. He was a bit surprised since he thought he’d made a personal connection to the professor that he’d auditioned for, but put it down to a cold reject. Some years later, he crossed paths with the professor, who remembered him, and asked him why he’d never responded to the offer. It was then that he realized what had happened, and then sued and settled with, by now, his ex-girlfriend.
Edit : https://www.cnn.com/2018/06/15/us/dream-school-false-rejection-letter-trnd/index.html
I found the news article - this guy was in fact a clarinetist, and it was worse than I remembered, she actually faked a rejection letter.