Just ordered a set of Cooper Discoverer A/T 3 235/70/16's and was looking to pair them with some Black 16x7 Cragar Soft 8's with 4" of backspace. Will these rims work without a lift?

Without a lift the backspacing will most likely cause some rubbing.

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03 Sport - SEMI DIGGERIZED, Surco Rack with Daylighters, OME Lift, Runcool Hood Louvers, RL Front Bumper and Super Skink Sliders, 31" BFG AT/KO on Soft 8s, Skid Row/Mopar Skids, 8k Smittybilt Winch with Synthetic Line.
MY BUILD: viewtopic.php?f=3&t=59628

Is that because of the tires I picked or does it have to do with the backspacing? Rubbing just when turning or all the time? Could the rubbing be dealt with or would it ruin the tires?

The tires are fine, its the back spacing on the rims that will get you in trouble. If you arent lifted try staying as close to stock when it comes to back spacing. You should only have rub during turns.

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03 Sport - SEMI DIGGERIZED, Surco Rack with Daylighters, OME Lift, Runcool Hood Louvers, RL Front Bumper and Super Skink Sliders, 31" BFG AT/KO on Soft 8s, Skid Row/Mopar Skids, 8k Smittybilt Winch with Synthetic Line.
MY BUILD: viewtopic.php?f=3&t=59628

Backspacing unlifted its best to stay as close as possible to stock
Tire / wheel combo will sit out and hit flare/bumper/pinchweld etc
If you want to hack away enough plastic they may work but i wouldn't do it
Paint your stockers, save some bucks and install 245-70-16s

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MUDD'S MOTORSPORT'S We do IFS lift installs ,
03 OVERLAND EDITION /Kilby-Skidrow-Mopar-4XGuard skids/ 2.5 inch TOTAL CONTROL JBA coilovers -JBA Arms/MOABS-31 FALKEN WILDPEAK AT3W / 4.10's etc, 04 Kilimanjaro Edition loaded, plus 05 KJ limited