Yes, there are issues. The difference in size is about 10%. You have a "gear" (tire) that is ten percent different on the opposite side of another one (35" on one side, 32" on the other). You're introducing a ten percent difference between two sides of the differential. A differential is supposed to allow for "difference" between the two axles coming out of the differential; however, that's introduced as normal driving conditions, turning for example. That ten percent difference you're introducing is causing addition wear (work) for the differential. Your tires are going to wear funny.
When the lockers are locked, there is no change or difference, the differential that allows that difference is now locked together. You are introducing a ten percent difference on each side of a locked differential. You're essentially taking something that is locked together and trying to twist it at different rates. The weakest link will have to "give". Hopefully you're only going to get tire squealing, but you're likely to break something when you get to hard surface driving.
If you have a part-time system, you can get away with it for a limited time as long as you're in 2-wheel drive without locking the differentials, but in an all-wheel drive/always on system, you're working it much more.
Take a broom handle in your two hands and now try to twist the broom handle at different rates for each hand. Your hands, or the paint on the handle, get chewed up. The handle isn't going to twist at different rates until it breaks. So, the weakest link, your skin is going to heat up and blister. That's what you're doing to your drivetrain, axles, differentials, driveline, t-case; heating and beating them up.
I asked this a while back and a few people suggested a 35 inch spare is fine if I run 37s all around. I don't want to deal with all the extra tailgate weight and moving the light, etc if possible. That said, If I were going 35s all around I would stick a 35 on the back because it will fit fine, work better and look cool
I'm not certain that your typical donut spares are the same circumference as all the other tires and that works fine in a get you home type scenario
A 32 would be OK and drivable. Just like the little donut spares you wouldn't want to do it more than necessary. Handling wouldn't be great, but you'd get by. You wouldn't damage the vehicle so long as axle wasn't locked or in 4x4 on dryish surface. Your Bronco would "think" you're just driving in a continuous circle. Really spares are used so infrequently anymore, it really hardly matters.
I usually wait til the second tire change then swap out for the proper size...just me...cheap.
Its done all the time as long as its not a drastic difference 33 works for 35 ,35 for 37 no problem especially if elect locker,detroin might be noisy.
If worried put one of the fullsise on rear and put smaller in front drive in 2wd just fine.
I have driven miles with a broken spring hanger and winch cable wrapped around it ,if you wheel you will break stuff dont be scared to improvise,adapt,overcome.
For a VERY short time in a pinch in college I ran 2 one size smaller on the same axle (two flats and used 2 cheap used tires until I saved enough for correct tires). HOLLY HELL just that made ABS and traction control go bonkers...it was bad. I could not imagine running a 32 with 35's on the other 3.
I don’t know what the size difference limit is but many new suv‘s have a speed sensor in each wheel to detect when your in a skid or lost traction. If one wheel is spinning too fast compared to the other tires the computer might “think” your in a skid especially when turning. The computer will apply the brake to correct the speed offset. If it thinks you are in a skid it will try to bring the vehicle back in control. So you may not be able to drive the Bronco on the highway or in the situation you describe.
If you have a fairly new car, accelerate on a wet road and the computer will activate traction control by applying brakes and/or killing the throttle until the wheel stop spinning. It does this because it detected wheel speed differential between the wheels (driving wheels spinning faster than non driving wheels).