I know Auburn says not to use synthetic, and that they won’t say why. Now Dirtydog said something about conventional oil working better with the clutches in a LSD, which would seem to make sense. Now my question would be, why would Auburn say to use non-synthetic oil only, but Dodge recommends synthetic? Doesn’t the stock LSD in the Ram use clutches like the Auburn?

the only explanation I got from the shop was that if you use synthetic, it wont lock up as well/at all. Perhaps the "at all" was a little inflated truth, but I beleive it wouldnt lock up "as well". Synthetic oil has a lot more microlubricants and other things put in it for longevity.