All class items that are not specifically assigned to factions should have the option on where your reputation goes. I have a lot of really awesome Hunter Cloaks and Warlock Bonds that I would love to wear but don't because I want rep. gains for factions so I can get shaders and I don't want to accidentally do a nightfall or something with a cloak that will give me vangaurd rep.
Would be cool if you could press y or triangle for details on class items and on the right hand side (or anywhere) it would give you the option on where to assign that cloak (not permanent so you can at any time change where the rep goes). This would also (very slightly) add a bit more diversity in the Guardians and would allow for a little more creativity/customization.
Edit: Or you could take any class item to whichever faction you want the rep to be applied to and they could add a little symbol on it for 2 motes of light or something along those lines.
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I think it would be better to have a choice between which faction items give you faction rep. Like the ability to set their banner as your tie to their faction or the Chest plate or something like that. So everyone can still see who you ally yourself with but you can customize your look more