They get to claim it because we let them. Every time an article comes out with "____ is a Nazi dogwhistle," there's a set of people who don't want to be associated with Nazis (or insert relevant disliked group of choice) who will immediately drop whatever the thing is. This creates a cycle where something does eventually become a dogwhistle, because everyone who didn't use it as such has stopped using it altogether.

TL;DR: Fuck 'em. Don't let those assholes control how you express yourself.