So let's address your point first, then I'll add anecdotal info for you:
This post isn't about the Nazi party, it's about fashion choices going out of style because of crimes comitted by individual(s). The toothbrush moustache is a style of moustache in which the sides are vertical (or nearly vertical) rather than tapered, visually resembling the bristles on a toothbrush. First becoming popular in the United States in the late 19th century, the style spread to Germany and elsewhere. After Hitler had done what he had done, the toothbrush moustache had lost all of its popularity.
As such, you don't see people wearing red caps that much anymore unless it's a MAGA cap. I recognized this when my wife and I watched "Father of the Bride" with Steve Martin where, in the first scene, he is seen having a red cap with the same form as the MAGA caps. It was such an eyesore, and we couldn't look at it any other way - in spite of it being an 80s/90s movie.