Will magentic snaps on bags cause my credit cards to stop working?

Yes, long exposure to magnets regardless of its power can demagnetize the strip on credit cards. However, this is rare for bag snaps as they usually don't come to close to the actual strips (especially if the cards on in a leather holder with no magnets).  Basically, the magnet has to be less than half an inch away to the card with nothing between (direct exposure) and remain there for a significant amount of time (several hours). But even this does not ensure demagnetization.

So basically magnetic snaps are quite harmless to credit cards because they are obstructed by thick canvas and/or leather, small in size and not usually right up against your credit cards.  It's much more likely damage is done by magnetic snaps on wallets.

I carried many bags with magnetic snaps for the last ten years and have a non-magnetic leather card holder for my credit cards or use a metal money clip. I've only ever had two cases of demagnetization, both caused by security check devices.