The closest you can get is step 1 of setup:
Players agree on which factions to control. One player controls Rebels while the other controls Imperials. If players cannot agree, randomly assign factions.
However, this is generally due to component limitations. If you really have 16 TIEs and want to fight an imp vs imp swarm or a rebel vs rebel skirmish, whose to say you can't?
There's also nothing stopping you from fielding Luke and Vader in one father-son tag-team squad if you really wanted. You couldn't do it in a tournament, though. It's actually kind of weird that the tournament rules are more permissive about mirror matches than casual play by the rulebook.