But not to any great extent. Especially if you're not driving your vehicle many miles a year.
It's correct, that most large chain stores are not going to mount them on your stock rims for just the reason cited. The tire manufacturer's recommendations.
Not surprising though, since these days a 7" wide factory wheel is more the norm than it was back in our vehicle's day.
With a Bronco, there have been many, many people running that size tire on the stock wheels. Not to say they were perfect, or that they didn't wear a little more in the middle (especially if you didn't modify your air pressures), but it should work.
But will it fit without rubbing? I can only say with 90% certainty that they will. Over the last 50 years or so, we've certainly seen some that rubbed. But I've known far too many people with 31x10.50's on their uncut Broncos with no rubbing to say it's not going to work.
If in doubt, mount just one up and install it on the rear right there at the shop. Test fit it to see if your Bronco is going to be one of the normal (does fit) ones, or one of the oddities (does not fit) ones.
Oh, and while you're in the decision phase still, I would measure your axle-to-frame clearance to make sure that you're not sagged down a bit already. The loss of an inch or so in original ride-height might just make the difference.
You're looking for 7" in the front, and 6" in the back, between the frame and axle tube. Any less than that is your sagged height less than stock. Approximately....
If it's sagged a bit, and you carry passengers, I could see a 10.50 occasionally rubbing on bumps and such. Especially if you carry adult passengers. Kids don't seem to cause much drama.
Well, in the ride-height department that is!
Paul