If I were to wager a guess, I'd guess that the targets of the term 'alt-right' would rarely accept that description of their politics. Whereas 'right' or 'conservative' or 'social conservative' or similar terms would have a high acceptance rate for those that are being called it. 'Alt' has become a pejorative in everyday use (at least in the liberal circles that I run in).
I am a proponent of aiming for accuracy when trying to describe other people's politics, and being charitable whenever possible.
If I see a group of people using words to describe another group of people in a way that purposely misrepresents them, particularly in a negative way, I think that's something worth calling out.
I don't have the nihilistic take that "if you can't 100% accurately describe something, then it's okay to not even try".