It's not the symbols of Nazism that were the problem. It was the murder and constant destruction to accomplish the murders that people rejected. Symbols may or may not say a group using them are the same as Nazis but they are a head's up for such thinking. Combine the swastika with a raised-hand salute and it's a dead giveaway.

Hitler ruined everything. The word ‘Fuhrer,’ Wagner’s music, some verses of the Deutschlandlied (Deutschland Uber Alles), and yes, the swastika, all predate Nazi Germany. But their association with Hitler has irrevocably tarnished them.

Playing on the uninformed idiocy of morons.
The sun sign, crux gammata, gammadion or Hakenkreuz. Ironically the word “swastika derives from the Sanskrit word svastika, which means “to be good.” and was not a word used by the Nazi's, it was an an invention of the british propaganda department who thought that the irony was amusing and that the word sounded sufficiently nasty.
I remember a few years ago islamist Muslims using exactly the same trick to demonise Hindu's in the west by calling them anti-Semite and nazi for the use of a three thousand year old Hindu symbol