My cat had kittens two weeks ago. Yesterday, my neighbors were fighting pretty loudly and since then she's been hiding her kittens in a closet. Could the fighting have scared her into moving her kittens?

Absolutely. Your cat's senses are already heightened because of being a new mom and your jerkwad neighbors need to be told if they can't keep it down you'll call the cops.

Let your cat stay wherever she has taken the kittens, because that's where SHE feels safe. If possible, you may sit near there and read or lie next to the area. Let her know you are there to help protect.