Hello Bandit,
Currently, Spektar Faction Class Items cannot be used for the exotic faction quests.
Bungie is aware of the issue and are investigating a fix.
https://www.bungie.net/Mobi/en/About/Article?id=44590
In the meantime, equip a non-Spektar bond for your Warlock, and you should be good to go!
English
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So I think this is still broken? I have new monarchy cloak shader and emblem but nothing is registering for the first part of the quest