I want to get some 15x7 steel wheels for my 87 pickup. I plan on running 31x10.5 BFG MT. I have no lift. The back space options are 3.75 or 4.5". I don't want the tires to stick too far out, but I'm concerned that 4.5" will rub while turning. Any advice?

 

If you laid the rim down on the ground, pretty side up, the backspacing would be the distance from the ground to the face that mates up to the axle/hub. That means that the 3.75" backspacing would stick out farther than the 4.5".
If you ever plan on a suspension lift such as ball joint spacers, you'll need less backspacing so the rim / tire doesn't rub on the upper control arm so you may want to go 3.75" to future-proof it.
Either way I'd ask the tire shop to mount the tires and test the clearances. Either rim will likely let the tire rub on the fender if you don't have any sort of body lift installed, when you have the tires at tight angle and hit any sort of significant bump.