What could cause a Chevy 305 to foul out the spark plugs?

Needs a new carb. Replace the old one with a new reman. I had the same problem after a batch of bad gas

That is a good possibility, but you should also be on the lookout for weak ignition such as a bad cap and rotor, bad wires, bad coil.

I've also encountered this problem when the valves are not sealing against the seats good. Only solution for that is a valve job.