Why in your view is it mutually exclusive? To address any problem one first has to identify that there is in fact a problem. Calling it out where it exists IS that identification. It isn't about "labels" it's about identifying what needs to be dealt with and make no mistake there are a lot of people who don't want to acknowledge the problem and if anything what you're doing is exactly the shit the fascists do by forcing the side wanting to fight fascism to moderate its language on the belief that if we use that language against the fascists the fascists will dig into their fascism... as if they aren't doing that anyway.
In fact letting the right-wing control the narrative no matter what happens is in large part why we are where we are and why this shit needs to be called out, identified, labelled and opposed at every point with whatever means are necessary.
I'm sorry but what? This is really weird logic as language and words aren't required to follow some linear path of severity. People call the GOP, Trump and the like Nazis because... they fit the definition of Nazis, actual card carrying Nazis support them by a significant majority. (Yeah yeah I know there is the odd one here or there that doesn't)
If it walks like a Nazi, talks like a Nazi and engages in Nazi tactics, behaviors etc. Then it can be called a Nazi. You don't reserve your language so that you have some end point to progress to.
It's also very weird to use the boy who cried wolf when the whole point of that story is that you don't call something that which it isn't for fear that when the real thing comes along no one will believe you as that would imply that they are in fact not Nazis. Which would only be true in the most technical of sense (As in they are not of the Nazi party of Germany) but by most dictionary definition the word fits.
Lastly, what the hell are you even talking about "edgy"? Do you think people are calling them Nazis to be edgy? Because that's ridiculous and quite frankly your entire comment screams of someone trying to defend them through deflection.