From my experience comes this.
On my stock 87 XJ, I currently have 235s, with room for more. A 2" lift will fit 31s fine for me, and I could wheel it.
On my 89 XJ that I previously had, I ran 31s with a Rancho 2.5", and wheeled it plenty. Lot's of travel and plenty of room. The tires were 31x9.5 Swampers on stock rims. So they didn't stick out past the fenders and tucked up into the wheel wells.
Then I added 2" of budget lift and ran 34x10.5 Swampers. Again, no problems off road. Total of 4.5"s of lift.
Biggest mistake that people make is getting REALLY wide tires AND changing the offset of the rims. Now the tires stick out really far and rub when you try to wheel them.
A 31 on a stock rim SHOULD tuck up nicely if you plan to wheel your XJ.
You can look at 32x9.5 or 32x10.5 swampers with a 2.5 or 3" lift.
PM me if you want more info.
I'll say this again, this is just my experience, and is not gospel. Others will have different experiences with their vehicles. They are not wrong in what they say, and neither am I.
Erik