i have cut a crapload (i think 400 sheets or so) of gator board (which is a denser version of what foamcore is) and a little bit of foam core on a laser cutter at work (not the GF, an industrial cutter, but still CO2). we use it for a base in between layers of cans when building canstruction structures.
from a fume perspective, it’s not an issue. it is a flame risk, for sure. but honestly, if you’re monitoring it the whole time (and I was), a spray bottle of water and a towel will take care of any flareups. i saw a few times where we had a sharp corner that there were red spots (like where you would see coals in a fire) but they all self extinguished quickly and we didn’t have to pause the jobs. but if we had, i’d have spritzed it with the water bottle and pressed the towel onto that spot.
so the real key is literally watching it the whole time it cuts. if you can’t do that, i wouldn’t cut foam core.