Customizable character, animating clothing, etc.

If I have a character who’s clothing & such can be customized in-game (Using sockets), how does one go about animating the clothing to conform to the player’s skin?

If your cloth meshes are skinned to the same skeleton as your character model you dont need sockets. Just add skeletal mesh components to your characterBP and set their master pose component like so:

So the clothing needs to be a skeleton? (The shirt is a skeleton with only a mesh in the torso area, etc.)

Yeah it needs to be a skeletal mesh that is skinned to the same skeleton as your body mesh. When you import it you need to import it to that skeleton too.