Using a syn isn't going to hurt the truetrac in terms of damage, but it will slightly degrade the torque bias performance, and since that is what you seek in a traction control diff, why use something that will reduce the effectiveness? The same applies for the FM additives; they don't "hurt" the equipment, but they alter the performance in a negative manner to some degree (would vary based upon the amount of FM, basestock, etc).
There are a LOT of lubes that meet the SAE J-2360 performance spec; both dinos and syns. Why not pick one from that list, which neither is syn nor has FMs?
current listing here:
http://p-r-i.org/other-programs/automotive-qpl/lubricant/
current list was just done early this month
It would behoove you to check the product sites for the most recent info because some of them have FM in them in the bottle, and you'd want to avoid that.
Obviously a syn will likely last longer in service, but the dino lubes on this list have passed the very same strict and stringent (Mil-spec equvilant) J-2360 tests as do the syns.
So, my recommendation is a conventional lube, in your desired vis range, that does not have FM, that meets your favorite brand flavor.