Often, when the police tried to break up the communist/nazi brawls, they'd band together to fight the cops.
Honor among thieves (or lack thereof), and besides, Karl Marx pretty much indicated that killing each other was going to be inevitable and in fact exactly what they should do when they take power akin to the Reign of Terror in France (and based on what Grignon stated about how they are to kill everyone they find even if they were fellow Republicans, it’s pretty clear they were going to kill even their own allies for a sheer laugh).
And yeah, they definitely would fight against law enforcement, since they hate the law.
Actually, that reminds me, nowhere in the Prequel Trilogy of Star Wars did they really get into that kind of thing with the Commie/Nazi brawls regarding similar analogues.
That's what happens when you try to break up a fight between brothers.