That's the standard shim that comes in all TJ Rubicon Dana 44 axles, all come with that exact same shim for the Rubicon's carrier/locker. There's one on the other side too.
When the carrier bearings are in good condition, it takes quite a bit to seat the shim as you can see from the BFH I'm using below. This shows the driver's side shim which is similar to the your loose fitting passenger-side shim.
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I didn't see the edit to your post yesterday. Thanks for additional info.
Again, I may not have described the situation in my original post very well. When I said that i could move it freely, it was not just dangling - I did have to exert pressure to move it up the 1/4th of an inch that it was out of place. I did take a brass drift and BFH to it and it took a lot of work to get it in. It does sit in there snug, just over time it will sag a little as if it is off by 0.001-0.002".
I wasn't in a position to pry out the carrier yesterday, but with both axle shafts removed - it was in there snug enough that I could not pull it straight back (I did use a wratcheting strap to prevent it from flopping out, just in case - when I had the diff cover open and removed both rear axle shafts).
The bearings and R&P are about ~23K odometer miles old (my odometer is greedy wih larger tires, adding .15-.16 miles per a tual mile driven due to larger wheels).
I had decided to let the gear oil go longer, since the last couple of changes when I saw that surface rust issue was under control. I only Royal Purple 75w140 in my diffs, sonif there is a leak - I can spot it easier. That shit isn't cheap though, and neither are Lube Lockers (which I jave only reused once between 1500 mile gear oil changes, I don't like taking chances).
There was just a little faint metalflake paint-like content stuck to my drain plug, and a tiny fragment of the drain plug threading that chipped off (that's another story).
The wear marks on my R&P look nice, perfect even according to my guy. There wasn't any signs of bearing damage that merrited taking it out.
IF things were to go south, I am anxious to swap the R&P, bearings, and probably axle tube seals (because why not) myself. I can probably get the former ARB guy to help if I were to plan it ahead of time, I don't know him well, he is a friend and former coworker of my Jeep buddy and he helpd him get an ARB in the front of his YJ (so I don't want to burden the guy right now). My area is pretty sad for shops that would be able to do this job anyhow, like damn near everything else that I have done on my own - I'd have spent $50K in labor alone.
I will keep driving on it as I have.