I talked to my guild, to players that have all done Tributes we looked at all my pursuits, progress etc. and can't figure out why these are locked. (see screenshot) I've got 4 boons turned in, I've opened all the chests on the barge. I've run menagerie several times. I can place the first banner in the Tribute hall and none of my doors are open. People have asked if I opened the chest at Werner on the barge. I don't know if I did or not but it's not there now - so I am thinking I did?... That or it's missing. I've walked the Invitation quest all the way through and the invite is no longer in my pursuits.
In the picture, the tribute you've highlighted to buy is locked due to you not having enough Dusklight Shards in your inventory to buy it. With that said, Bungie is aware that the Tribute Hall is not working for some players and is investigating. This is listed in the known issues sticky post at the top of the help forum. I'd check the other items in his inventory to see if you lack the resources to buy. And how about the Triumphs, have you claimed any of the Tribute Hall Triumphs? Most of those award tributes as well.