Can I skip the foam board and just use Rockwool against my basement block?

Your contractor is fundamentally wrong about the 'breathing' aspect, and following his plan in Climate Zone 4A is asking for a mold colony behind your drywall in five years. The issue isn't whether Rockwool is hydrophobic—it is—but that it's air-permeable. Warm, moist interior air will migrate through the batts and hit that cold CMU wall, where it will hit its dew point and condense into liquid water. Since the framing is already there, it creates a thermal bridge that makes those spots even colder. You absolutely need an air-impermeable layer like **XPS or foil-faced polyiso** taped and sealed against the block. This keeps the humid air from ever touching the masonry. If you just shove Rockwool back there, you're creating a chimney effect in that half-inch gap where condensation can run down and rot your bottom plates. Even if the Rockwool doesn't soak up water, the dust and organic matter on the surface of the block will grow mold once that moisture is present. Moving the walls is a pain, but it's much easier to do now than after the electrical and drywall are in. You usually just have to back out the Tapcons or cut the powder-actuated fasteners on the bottom plate and slide the assembly forward. I'd aim for at least 2 inches of rigid foam. This gives you a continuous **thermal break** and moves the dew point into the foam where it can't condense.

Before you move everything back, check the exterior drainage and make sure you don't have active bulk water leaks. If the wall is bone dry, go with the 2-inch foam, tape the seams with high-quality acrylic tape, and then snug the framing back against it. You’ll lose a few inches of floor space, but you'll have a basement that doesn't smell like a swamp in ten years. Tell the contractor that the building science on this has been settled for a long time; 'breathable' assemblies in basements are a relic of the past.

I did exactly what your guy is suggesting in my last house. Two years later, I pulled a piece of trim and found black spots all over the drywall. That half-inch gap just traps stagnant air and makes everythign smell like a swamp. I ended up prying up the bottom plates and sliding 1-inch XPS back there myself. It took a Saturday and a few cans of Great Stuff to seal the edges, but the difference was night and day. My current basement is bone dry and acutally stays warm. Don't let him talk you out of it; moving a few 2x4s now is way easier than a full mold remediation later.

This is all pretty scary to read becuase I barely know the difference between types of insulation. I'm just starting to plan my own basement, and I always assumed 'breathable' sounded like a good thing? If you move the walls out to fit that foam, does it make the room feel alot smaller? Also, if the contractor is alredy this far along, is it hard to get the electrical boxes to line up if you shift the whole wall forward? I'm worried my guy might try the same thing and I won't know how to catch it.

Don't overthink the labor; just grab some Owens Corning FOAMULAR NGX. I had to do this exact fix because my guy tried the same 'breathable' nonsense. I made him pull the plates and we slid 2-inch FOAMULAR boards right behind the studs. It’s the pink stuff you see at the big box stores. Tape the seams with 3M 8067 and you’re golden. It’s way better than letting the Rockwool touch that cold block. It only eats about two inches of space, but the peace of mind is huge. If you don't use a dedicated rigid board like that, you're basicly just building a mold farm.

Ugh, the 'breathable' excuse is such a classic contractor cop-out. If he's worried about the wall drying, tell him you'll use a smart vapor retarder like MemBrain over the studs instead of poly. But yeah, don't let him skip that rigid foam. Since he only left a half-inch, he's prolly just lazy about re-cutting his top plates. If you've got a French drain or a sump, make sure the foam doesn't block the weep holes at the bottom. I'd also check if he used pressure-treated wood for those bottom plates—if not, they'll rot out twice as fast once that condensation starts dripping.