When a word is too flimsily used against people, it loses its meaning. This is what happened with calling people racist. It got tossed around inappropriately so much, the public lost their sensitivity to it. People now roll their eyes when someone accuses them so casually of being racist. Therefore we have a new word to level at people, Nazi.
The same thing will happen with calling people "Nazi". Initially people will be scared that they will lose social capital if called a Nazi. Eventually, people will have seen enough obviously non-Nazi folk be called Nazi, that the word will again lost meaning and power.
Nazi will fall faster than other social weapons, simply because it is so ludicrous. When they level that charge are they really suggesting the person follows the National Socialism doctrine? That they advocate for mass genocide? That they follow the numerous ideas of Nazi-ism? They have a strong position on Anschluss? This is bizarre (and amusing) watching from a European perspective.
There is a much more widely held ideology that is closer to what the left perceives the right to hold, but it would Never fly to accuse people of that..
edit: I fully agree with the parent that the term being used in the way it has been is Incredibly insulting to those who suffered under the Nazi regime.