I don't think a group should keep track of add-ons in it that are off, just add-ons that are on. People group add-ons into as many groups as they want. Then they turn on the groups they want. All the mods from the group are enabled. If a mod is in a single group that is enabled, it is turned on, even if the other groups it's in aren't turned on.
Suppose I have two groups. Pirate weapons and ninja weapons. Pirate weapons contains a sword and a gun. Ninja weapons contains a sword and a staff. If both Pirates and Ninjas are turned on, the game will have swords, guns and staffs. If I only turn Ninjas on, the game will have swords and staffs. If I only turn Pirates on, I will only have guns and swords. If I have none on, I will have no weapons.
Alternatively, a checklist system. People load checklists and it automatically enables all of the mods on it. People can then turn off the ones they don't want or disable all addons and start from scratch. The game should come with a default addons checklist. No dealing with priorities or multiple groups, it's just a simple script that enables all the addons in it and skips the ones that are already enabled. Checklists should not be able to disable addons.