By assigning moral outrage to one side of the debate, we remove the pretense of a debate. It's no longer about evidence and facts but vilifying one side. It's ad hominem 2.0 if you will, and it works because we as a society have a visceral negative reaction to some labels.
The problem is that pavlovian-esque training can be untrained. If you call everyone who does something you don't like a nazi, then pretty soon it doesn't seem like being a nazi is all that big of a deal. That in itself is bad because by abusing the term you buy cover for actual, literal nazis. The same issue applies when you label everything racist or sexist or otherwise.
Words have power, but that power can fade if misused.