Such crossings are pretty rare in NYC, and even rarer in passenger routes there.

https://commons.wikimedia.org/wiki/Category:Level_crossings_...

State/local governments can also declare a quiet zone. https://railroads.dot.gov/railroad-safety/divisions/crossing...

Quiet zones require crossings to be up to a certain standard. If the people opposed to train noise were serious, they could pressure their local/regional gov to upgrade crossings and establish a quiet zone. This tends to be more successful than trying to prevent the train entirely.