It's been valuable to me to know where to buy touch latches and other cabinet hardware, because I can call them up and get the phone number of the manufacturer. Find one. Phone the manufacturer and ask what they would do to eliminate, not just mitigate, noise from the latch.

Foam or anything else you're thinking of has one thing in common: it puts the latch under just enough stress that the door can't move. I'd say the thing to do is to provide enough tightness that there's not a rattle, but not enough to strain the latch; this is where the manufacturer can probably help you.

Also, foam will compress and weaken with time; perhaps small felt dots are a better answer.