Did almost exactly this in my basement a couple years back, and the framing stayed put. Cut rigid foam sheets so they fit snug in each bay and pressed them right against the block. Don't leave gaps and hope the batts hide them, because air leaking behind the foam is where you get condensation. A bead of low-expansion foam around every edge does the job better than tape on a rough block surface.
For thickness, I left enough depth for a good layer of mineral wool between the foam and the drywall. Check what depth you actually have before buying board, that's the mistake I nearly made. The studs touching the block will still be a weak spot thermally, no way around it without continuous board behind them. But with the foam sealed tight to the masonry, the warm room air never reaches cold concrete, so the condensation risk mainly comes from sloppy edge sealing rather than the stud contact itself. I've had zero moisture issues thru two winters now.
If any bay sits below grade and stays damp, sort that drainage issue first. Foam against wet block just hides the problem.