I usually wear ultra thin wicking fabric
Champion boxer-briefs under my padded bike shorts. Works for me. I've tried both ways since the 1970s. With is more comfortable for me.
It's the same fabrics used in most cycling clothes. It doesn't defeat the purpose of the pads. And it provides better support. The Champion shorts have a breathable mesh pouch for Frank and the beans, so everything stays where it belongs but doesn't overheat.
But don't try that with regular cotton undies.