Running smaller size spares on jeeps is done all the time and has been for many years. Whether it is harmful to one's differentials has been argued ad nauseum.
FYI -
From the California Four Wheel Drive Association (Cal4Wheel) list of safety requirements for all sponsored runs:
However, from the list of minimum vehicle equipment requirements for participation in the Rubicon Trail Jeep Jamboree:
But then, the equipment list for the Jeeper's Jamboree over the same Rubicon Trail reads,
Based on the above, it appears that where and with whom one offroads has as much to do with whether one should run a full size spare as the potential for adverse effects.
Here is an exchange from a thread in another jeep forum with an answer to
@VAUGHN06TJ's question regarding running undersized spares from an individual undisputed as an industry expert and an authority on Jeep TJ's:
https://*****************/forum/f9/opinions-using-smaller-spare-tire-1138776/
I run 35" Mickey Thompsons, but my spare is an old 35" BFG MT from a previous set of tires. I need to replace the spare but I don't want to purchase another Mickey Thompson tire because my next set will likely be something else. Therefore, I intend to purchase either a 34/9R16 TSL bias ply (33.8" diameter vs. 34.5" diameter of existing tires) or a relatively inexpensive 255/85R16 MT (33.3" diameter vs 34.5" diameter of existing tires) for use as a spare. Either of these "pizza cutter" spares will get me off the trail in the event that a tire on the ground suffers a catastrophic failure without doing any damage to my axles so long as I leave them unlocked, and either will get me to the closest or even second closest tire repair facility once I hit the highway - also without doing any damage to my jeep.
My reason for going with a "pizza cutter" spare is to save weight and bulk. The difference in cost for the 255/85R16 is too small to matter; the 34/9R16 TSL actually costs more. I ran a BFG 33x9.50 BFG AT as a spare for many years in my CJ-7 rather than a 35" spare, with absolutely no adverse effects even with a Detroit locker, and would run that size spare now if BFG still made them.
And that's my opinion on that.