Unless someone made a mod for it, there is not - the loadout menu only works with one player and was hidden in coop mode in base game too.
Thanks for answering! The menu was hidden but whatever was selected still worked. So I could still set a loadout for all the characters, and if we wanted to change I could quickly go into the singleplayer menu to change it. Is there any chance that something like this could be implemented? Every player starting with whatever loadout they (or the host) set in the singleplayer menu I mean.