How do I keep my folding workbench from wobbling when I'm cutting?

The issue is almost certainly the lack of diagonal bracing on those U-shaped legs. Barrel bolts are great for keeping the legs from folding back up, but they provide zero resistance against lateral force. When you're pushing a 3/4 inch sheet of oak, you're putting alot of horizontal pressure on the frame, and without a triangle in the geometry, those hinges and bolts are just going to pivot slightly under the stress.

You should definitly add some plywood gussets or diagonal struts to the leg assemblies themselves. Even a small triangular piece of 1/2 inch plywood screwed into the corners where the vertical leg meets the horizontal cross-member of your 'U' will make a massive difference. If you want it truly rock solid, run a removable cross-brace between the two leg sets once they are deployed. I found that just stiffening the leg units themselves ussually solves 90% of the racking.

And for the driveway issue, the two-inch foam is the right move, but make sure your saw depth is acutally dialed in. You only want the teeth clearing the wood by about an eighth of an inch. If you're plunging deep into the foam, you lose some of the friction that keeps the sheet from sliding, which might be why you're feeling more instability than usual. The foam should act as a high-friction bed, not just a sacrificial layer. One trick for those folding brackets is to shim the gap between the leg and the apron with a bit of scrap laminate or even heavy cardstock. If there's any air in that joint before the barrel bolt clicks into place, it's going to wobble. Tighten up those tolerances and add the braces, and you'll be able to manhandle those heavy sheets without the whole station shifting on you.

I’ve got a similar setup and the real killer is the driveway slope. Unless your concrete is perfectly level, one leg's always gonna be off the ground. I ended up swapping those fixed legs for some adjustable feet I found online. Total game changer.

Also, if you’re still feeling some drift, throw a couple sandbags over the bottom cross-bars. It adds enugh mass that the table won't dance around while you’re pushing that heavy oak. It's way easier than rebuilding the whole frame.

Ditch the barrel bolts and swap in some Starborn structural screws if you’re modifying that apron. For real stability on a driveway, I went with the Bora Centipede CK9S—that 4x6 workstation is rated for 3,000 lbs and doesn't flinch under 3/4 inch ply. If you're stuck on the DIY frame, check your hinges. Cheap 3-inch piano hinges have too much slop; you want a heavy-duty 14-gauge continuous hinge to kill that side-to-side play. Also, are you using a track? Running a Makita SP6000J on a 118-inch rail keeps the weight centered so you aren't fighting the table's physics as much.

You might examine the coefficient of friction between your two-inch foam sacrificial layer and the actual plywood surface of the table, becasue if you are utilizing extruded polystyrene, it can act almost like a bearing surface against smooth ply, allowing the entire workpiece and foam assembly to migrate laterally during the feed stroke. I found that applying a series of adhesive-backed non-slip strips or even a light dusting of spray adhesive to the underside of the foam ensures it remains registered to the table, wich prevents that disconcerting micro-shift that occurs right as the blade engages those dense oak fibers.

So I tried adding some diagonal bracing to the legs like several of you mentioned, and it fixed the sway imediately. I also swapped those barrel bolts for structural screws to tighten up the apron. It’s finally rock solid even when I’m pushing heavy sheets. I hadn't even considered the friction issue with the foam, but a few clamps solved that too. Thanks for the help!