I think it only semi-creates a desensitized reaction in theoretical discussions. I seriously doubt that, if a new-world Hitler were to rise to power, that people would turn a blind eye because language has evolved in using “nazi” as a slang term for adamantly hostile in regards to a certain movement or behavior.
As far as it making it harder for people to point out actual Nazis? Strongly disagree. You would have to be woefully uneducated to confuse what an actual Nazi is, in the historic sense. But, the way America is going, I wouldn’t doubt that. But I blame that on the poor educational system rather than evolution of slang.
Is it in bad taste? I mean, Soup Nazi from Seinfeld is one of the most quoted skits in all of sitcom history, written and acted out by all Jews. I’m in a part of the country where we have Jews a’plenty. I’m friends with, and have been friends with many of them throughout my life. They, as well, have referred to the slang usage of “Nazi”. I also work for Hasidic Jews, and the owner himself has used this terminology himself. Doesn’t mean that if some new eradicative movement were to occur, that people would get confused and start running into walls.