Is there a multiplayer Chess GUI that allows you to choose the starting position? With a human vs. computer, simply set Stockfish to depth == 1 and play it. Or, you can choose another (weaker) engine.

With a human vs. human online, is it possible to set the starting position? If so, what is the website?
You can play it in https://lichess.org/editor.
Chose your default opening, or just customize it, then click in 'Continue from here'.
You can chose if you want to play with with engine or with a friend.