Sweet Sami!
I don't think it matters either way. The lockers don't care what kind of gear lube you run just as long as you run gear lube.
I run Mobil 1 synthetic in my diffs simply because I like that the synthetic handles cold temps better (gets really cold during the winters here) and lasts longer because I only change the fluid every couple of years. If I played in water more and had the chance of getting water in the diffs more often I'd probably go with a cheaper gear lube and change it more often.
I know guys that play in the water regularily and change the gear oil after every offroading trip. They buy the cheapest stuff they can find.
