Outside of Mutate abilities, is there any support for a Mutant theme? (I'm thinking in terms of the creature type, not the ability.)
Nope. You have the obvious Charge interaction with the mutate abilities, Processing Collar and the like. Other than that, you have The Farm which grants all Mutants a Pounce. However, most mutants tend to have secondary races and if you overlap enough of that, you can add synergy from it. Beasts and Draksar mainly.
Honestly i've been running a mutant bg, to some success, mostly focusing on their tankiness and the sl bonus. Yeti and persecutor are very tough, imo processing collar is kind of a waste of a rune slot, the farm isn't bad though. Definitely miss organ harvest on my mutant doctor though, the ability seemed so thematic on him, but what can you do.