|By dbking [CC BY 2.0], via Wikimedia Commons|
First, calling people "Nazis" who clearly are not Nazis dilutes the meaning of the word and diminishes its impact. When we then encounter an actual self-identified neo-Nazi (or a Christian pastor calling for people to be put in concentration camps), there aren't any labels we can use that clearly distinguish between him or her and everyone else you have mislabeled. Why does this matter? We need effective labels that highlight just how extreme these views are and that places the person who holds them in a small but important category. If everyone who disagrees with you is a "Nazi," the term loses its meaning.
Unfortunately, we've seen something similar happen with "racist," "sexist," "misogynist," and "Islamophobe." When everyone who does not share your views is a "racist," it becomes far harder to address actual racism. We need to be able to address actual racism, sexism, and so on. When anyone who criticizes Islam is "Islamophobic," you are making it less likely that we'll ever see the sort of reforms that need to take place within Islam. This is a problem. When everyone is a Nazi, no one is a Nazi.
Second, calling people "Nazis" who are not Nazis is not conducive to productive dialogue of any sort. There is little reason why the party on the receiving end of that label would bother to listen to anything else you might say. He or she knows it is not an appropriate label and that you've lost all credibility by using it. Instead of being receptive to your views, it seems far more likely that he or she will be more determined than ever to oppose you. It is difficult to see how this results in anything we might recognize as progress, and this is especially troubling when we agree with many of your views.
I suspect you have had the experience of being inappropriately labeled with some sort of over-the-top term that isn't remotely accurate. Maybe you are an atheist and that was sufficient to lead a Christian to call you "Satanist." When you finished laughing, my guess is that this probably didn't lead you to be more willing to consider the Christian's position. I suspect some of you on the left have had similar experiences with being called "libtard" or "cuck" by conservatives online. And once again, I'd bet that these experiences probably didn't lead you to adopt their point of view.
Third, your misuse of the "Nazi" label detracts from the important historical context of Nazism. There are undoubtedly some Nazis left today, but most are over 90. According to the National WWII Museum, no WWII veterans will remain by 2036. There are neo-Nazis around today, but they aren't Nazis. They haven't done what Nazis did. If we want to prevent a repeat of the Nazis did, it is vital that future generations remember the full scope of what real Nazis did and struggle with how it happened. Calling someone "Nazi" for something as trivial as disagreeing with some of your political views makes this less likely.
It is not difficult to understand why modern-day Klan or neo-Nazi rallies would make people uncomfortable, especially when one adds the sort of president we now have to the mix. And yet, I cannot see how the "Trump is Hitler" and "Trump supporters are fascists" claims are anything but harmful hyperbole that fuel the division, polarization, and tribalism most of us claim we dislike. When it comes to Trump and at least some of those who support him, it seems that we have more than enough to criticize without this sort of nonsense.