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From my own experience, I have done this and yes, they rubbed the frame. I didn't like that, so I changed to 31.5 tires. But I'm thinking now that I don't do as much driving, I may go back to 33 inch tires because they look so much better. Mine is an 88' 4WD truck.
Will depend on whether you are running 12.50 x 33's or 10.50 x 33's. I run 10.50 x 33 BFG KO2's on stock aluminum wheels on my 95 F150 4x4 and all I did was trim the front bumper about 1/2".
I've got 31x10.50-15's on the stock 15x7 wheels on my '87 F150. They do scrub a little on the radius arm when close to full lock when turning left. But not significantly, and I have a sneaking suspicion that the truck is due for radius arm and pivot bushings, that will probably stop that issue from happening. For whatever reason, no scrub when making right turns.
Before I put F250 springs in front, mine rubbed the plastic valence, until it finally melted out of the way, and doing it again, when I bought new tires, until I got the springs on it.