I understand I may get less IB rep but I don't need my crucible rank any higher and would rather increase my faction ranks instead
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Yes you will still get IB rep if wearing a faction item.
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Yes, you still get iron banner rep even if you have no iron banner items equipped. The class item, shader, and emblem for Iron Banner just give a boost to how much reputation you earn. Don't forget to switch your class item when turning in Iron Banner bounties though. Those only give Iron Banner rep, so might as well get the 10% boost for those.
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Yes, you can wear your faction gear and get rep for Iron Banner