Should I wipe my suspension fork stanchions with a wet or dry cloth after rides?

A damp cloth is probably the best option, but a simple paper towel is more than adequate. You don’t need to thoroughly scrub the entire stanchion. Just wipe away the ring of muck around the seals and anything on the stanchions that may remain. Be gentle; you don’t want to prematurely wear out your stanchions by overly aggressive wiping.