Currently, the only way to gain rep with factions is to equip their class item. Personally, I would like to raise a faction while wearing the class item of my choice. I feel greatly restricted due to faction rep grinding.
One viable change would be to make faction rep a buff instead of an item; that buff is then applied to the class item for a glimmer fee. This would allow players to wear whichever class item they desire while still raising faction rep.
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in the new dlc you can pledge yourself to a faction to gain rep, this makes it so you dont have to wear their class item, however ill still be wearing my signature version 1 new monerchy cape. its a status symbol of the fact that i was a new monerchy supporter from the beginning.