They are mutually exclusive. Both of them are fully-encompassed ideologies, not political buzzwords with a sentence-long definition.

Do you know what also never happened anywhere in world history? A communist country being fascist or a fascist country being communist. There was only one war because that's how long fascism survived before we (teaming up with communists) eradicated it. They were on opposite sides because they had diametrically opposed views.

Even if you only wanted to use the buzzword definitions, the people you're talking about are communists.