no lift on stock rally wheels rubs on lower control arms in full lock turns. 3" lift with 31s on 15x8s and no rubbing. without the lift it would rub badly on the wheel wells

 

I didn't say it didn't have any lift , sir; I only tried to say that I've kept the Jeep's unitbody and everything other than the leafpacks & coilsprings & shocks factory.
i absolutely have a 3" full lift kit on her . Everything above the wheelwell line retains the factory build from Oct of '94.

The OP inquired if anyone was running "...31" tires on a stock XJ" , but didn't say " running 31" tires with OEM suspension /no lift " , unless I misread...


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Just to make sure we are all on same page here, as-long as we are being ultra precise with what constitutes a "stock " XJ and what it'd involve running 31" tires on such a setup on our XJs; when we
see what was once - when it was new- a 31X10.50 x #" tire*- the OPs size in question on an XJ still being called a ' 31" tire ' when it is devoid of all but the final 1/16th of tread , it is agreed that it will measure out to likely more of a 28" or 29" tire by that point , yeah?
Just makin sure is all....


* (except for BFGs, of course ...you gotta get a 33" BFG before you can measure it at 31"... lol)

 

I think the fact of the matter is, one cannot run a 31" or bigger tire on stock height, unmodified XJ without worrying about *some* level of rub.

It's widely noted that the largest and most preferred size tire for a stock height XJ is a 235/75R15.

For me personally, I think the 235's look awesome, drive awesome and are a nice common size so your tire options are plentiful. I think anything bigger looks really ugly without a corresponding lift, but that's just my own opinion. I happen to also think lowered pickup trucks and low profile tires look absolutely stupid and ugly, but there are plenty of folks that are of the opposite opinion. I will always say, it's your Jeep, do what you want to it.

 

^This. @PatHenry I agree.
It has been over 15 years ago but , iirc, the installer at NTB or someplace back then told me the largest tire they'd put on a stock Cherokee was a 265/75r1# ...or somethin like that. My XJ had a set for a year or two of Coopers in that size but they were , like, all season or something, even though chunky mallcrawler tires...
I may be a little off on that.