You do NOT need to use friction modifier in a rubicon axle. That being said, pretty much all synthetic gear oil has it in it and if that's what you're using, it really doesn't matter.
As far as weight goes, I would use what is recommended in the manual unless you're running 5.13 gears or higher. At that ratio, I might consider a heavier weight fluid.
I've never heard that tip before (heavier oil with 5:13 or higher) - why is that?
Once the mechanics of the diff change so do the oil's requirements. Oil primarily does 2 things, lubricate & dissipate heat. As it gets hotter oil gets thinner & doesn't lubricate as well. The gear manufacturer should tell you what to run and how much once you upgrade.
manual recommends the heavier weight oil when towing (load). with all the add-ons and off-road use, I figure that's reason enough to use the heavier recommended oil to try and keep things as cool as possible.