Some west Texas ranchers in mule deer country will shoot any whitetail they see, anytime.
The whitetail bucks are more agressive about mating. Mulies tend to sorta hang out and wait for volunteer does, mostly. Also, they apparently go into rut later. Too much later, I guess. Early bird and all that...
SFAIK, in Texas, the "code of the west" is that a muletail is counted as a whitetail; that season is longer, more typically can be taken, and it's a help to the mule deer herd dynamics.
Art