I think Russia started the Nazi talk and Ukraine is bouncing it back at them - because as you said it's the biggest insult they could hurl at each other. They are justly proud of the high price paid to defeat Hitler. But it also turns into propaganda.
Russia started the Nazi talk because they're still very proud of the "Great Patriotic War" (WWII) and claiming it's a continuing fight against Nazis is good domestic PR. Not to mention the fact that Ukraine did historically have some issues with Nazi sympathizers (not surprising when you consider the crap the Russians put them through).
Ukrainians throw the Nazi talk back at the Russians because modern Russia is about as close as you're going to get to a modern Nazi state. They're not only riddled with far right open Nazi sympathizers, but their treatment of civilians is downright Nazi like, and their treatment of POWs seems to be as bad or even worse.
There is no right to privacy.
There is no right to your image.
Government can TRY to make those rights, but the freedom of expression is superior to the idea that you can stop me from hand drawing your image when you're at the beach.
One has to look out for engineers -- they begin with sewing machines and end up with the atomic bomb. -- Marcel Pagnol