My 05 Rubicon has an Dana 44 with LSD and I run straight RP 75w140. Zero issues and I had the RP in for close to 25K and it still looked clean and purple. On the RP and Mobil1 bottles they say fully compatible with LSD.
I've never had the rear end of my Jeep chatter with the RP/Mobil1 or Lucas 80w90/75w140 diff fluid. On my old 89 Mitsubishi Montero's with a LSD they did chatter and required an LSD additive, but at the time I also was running straight dino 80w90 gear oil vs full synthetic.
05 Electric Lime Green LJ with a 4spd Auto, 2.5inch Suspension Lift, OME Shocks, OME Steering Stabilizer, 32inch BFG M/T's on 17inch Moab's using Spidertrax Spacers, UCF Aluminum TC Skid, Novak Cable Shifter, Brown Dog MML, Rokmen 1/2 BL, Banks CAI, Diehard Platinum Marine Battery, JW Speaker 8700 LED Head Lights, Safari Nets, G.E.A.R Overhead Console/G.E.A.R Tailgate Storage, Rugged Ridge XHD Front Bumper, Warn Gas Tank Skid, Mopar Rock Crawler Rear Bumper, Warn XD9000i Winch with Warn Wireless Remote, and a Uniden 880 CB Radio