It's an ongoing, 200 page, flamefest debate on all of the 4th gen f body sites as to what can and cannot be used in Auburns and Eaton carbon fiber clutchpack diffs (what I have in mine).
I just threw caution to the wind recently and filled it with Red Line 75W-140 and the Red Line friction modifier.
So far, so good. NO; chatter, 'one wheel peel', or noise (even coasting around right hand turns!!).
I am not sure if the Auburns are even more sensitive to synthetics, so if you want to be very cautious, just use a VERY GOOD mineral based gear oil (Schaeffers, Torco, Lakewood, etc.) in either 80W-90, or if it is a noisy ring and pinion in your hot climate, an 85W-140.