That's just how Nuclear Throne Together works, but if you want the mod to auto-load when you go back into the game you can create a file in your mods folder called "startup.txt" and put commands (like "/load NTTE") in there which will run when you open the character selection screen
I'm not sure if there's much reason to go back to the main menu though besides settings, but you can access that through the pause screen if need be