The 265/75-16 measure 31.64" x 10.43" x 7.82" sidewall. They will fit with no issues at all on the stock JKs.
Up to 33 inch tires fit stock. You can't flex for crap, but doesn't require trimming.
Maybe AZKJ will chime in, he was running 33's on the stock suspension for awhile.
33's will fit a stock JK X
IF you trim the plastic air dam behind the bumper and don't mind a little rubbing on the back fenders whenever you hit a bump on or off the trail. The exception being is if you have the longer shocks that come with the towing package OR a Rubicon. There are three different shock sizes that Jeep puts on the JK. Mine came with the crappy short ones. For a few $$$ more I got the RE 2.0" lift and longer monotube shocks.
I have a '08 JK X. I'm running 285/75-16 BFG M/T KM2 (wanna be 33's... 32.83" x 11.22" x 8.41" sidewalls. As mentioned above, they fit, but they rubbed, especially when loaded down with trail and camping gear.
I went with a Rubicon Express 2.0" coil spacer lift with their longer monotube shocks. The front and rear bumpers are now 24" off the ground, the rock rails are 20" and the diff clears by a little over 13".
You must be registered for see images
Why Mopar lift etc? They are expensive. FYI... mods in them self do not void a warranty even tho some dealers may try to intimidate you into believing that crap. The only way mods void the warranty is if the specific mod has a "direct effect" on the issue you are having.
Another reason why I went with a 2" lift... anything over 3" and you start getting into drive shaft issues as well as beefing up other parts, extending brake lines etc etc. With the way my JK is set up, it is more than capable for the medium to slightly difficult trails I run.
Before the 2.0" lift and 285/75-16 tires...
You must be registered for see images
After the lift (same tires)...
You must be registered for see images
Flex with the stock Rubi BFG M/T KM 32" x 17" tires/wheels not disconnected and no lift (no rubbing issues)...
You must be registered for see images
Disconnected with 33's and a 2.0" lift...
You must be registered for see images
33's with a 2.0" lift do not rub...
You must be registered for see images
You must be registered for see images
One thing to seriously consider if you go with larger tires and go off road... re gear. I stalled on every rock that even looked at my Jeep with the stock 3.21 gears (a KJ comes stock with 3.73... go figure). I just had Yukon 4.56 gears installed. The difference is as different as day and night on the highway and the trail.
The old 3.21 gears on the left and 4.56 on the right...
You must be registered for see images
You'll find a lot of anwers to your JK guestions
HERE. A lot of people don't like the owner and how he runs his forum, but you'll find a lot of stuff.