I've been curious about this for a while, and all my research has provided no results...

Why do the West Coast Super Mutants have the leather straps holding their upper lip in place?

Easy one. It's this seasons fashion! Every supermutant want's to be hip!
I bet Tabitha started this line of fashion!

The writer of the Fallout Bible speculated on this --- I don't have it on this computer so can't refer directly, but he offered a couple of explanations -- like it being there to keep their big fat lips out of the way so they can speak (!)

It enables them to speak coherently because they have enormous upper lips from their FEV mutation that prevents otherwise. Why the FEV-V87 muties in DC didn't need the straps is beyond me. Then again, they didn't really have an upper lip, their upper teeth were always bared.

Ah okay, that makes a lot of sense... Thanks for the answers ^_^

So its like what? Like a retainer or braces or something but for Super Mutants? Maybe a Super Mutant dentist character somewhere is fashioning these leather straps for Super Mutants and would explain in detail exactly why they feel the need to wear them. I thought it was to emulate Super Mutant characters from previous games who seemed to wear the straps of combat helmits in their upper jaw because they wouldn't reach their chins. Hmmm...