I am also an amateur MMA fighter. As long as your lifting routine revolves around the core compound lifts(squat, bench, deadlift, pullup, etc), direct bi and tri work isn't going to hurt your strength or fight development. Strong biceps have actually helped me defend a few armbars(resisted the extension until I could move to stack or circle).
Powerlifters(who obviously rely almost completely on strength) do tricep work as an accesory move. MMA fighters don't(or shouldn't) rely on strength to that degree. Strength is one part of the equation for a fighter.
EDIT-If getting in skill work and conditioning causes a time crunch, then obviously bi/tri would be the first to go, with the exception of maybe some weighted dips. But if you have the time, who cares. I personally like having decent-size arms, so for me it IS more of a vanity issue, but I don't feel it detracts in any way from my training.