Please, do NOT conflate Ukrainian nazis with American right wing conservatives ... ever. It would demonstrate a dangerous misunderstanding of both. While such a mistake would save the nazis, it would be a death blow to American conservatives.
Wait, whoa. "our" Communists call anyone to the Right of Lenin a "Nazi" too. How convenient that anyone who disagrees with them is automatically a "Nazi" or the extended version, a "Neo-Nazi White Supremacist" (kinda like Larry Elder).
Dealing with the Enemy, Propaganda 101: You label them as something less than human in the eyes of your populace. For Russians, It's Nazis (Great Patriotic War), for the "Woke", It's "White Supremacist/Neo-Nazi", for ordinary "moderate Democrats" it's "Right Winged Extremist"...and the beat goes on. "Nips", "Huns", "Dinks", "Gooks", "Hajis", etc., by no means an exhaustive list), have been used by our own propagandists during wartime, too.
These stereotypes will be reinforced with political cartoons and images purporting to be in support of the stereotype, all in the interest of getting an entire population riled up.
For Ukrainians, "Communists" (as in Stalinist Communists) will evoke national memories of millions of Ukrainians forcibly starved by the Soviets in the 30s to save face for the government in Moscow when Soviet farming policies failed miserably, and now, "Russian" might be sufficient.
There is or will be a derogatory term for virtually any enemy used by those attempting to gin up popular sentiment against the enemy
du jour. (See Orwell, George, reference to "Hate Week" or "Two minutes of Hate".) Acting like every Ukrainian soldier in Mariupol resisting the Russian aggression is a "Nazi" is just basking in their propaganda stream