I found a few other issues with the dying system. Probably not the highest priority either, but here's a video:
https://www.xbox.com/play/media/3X8HZXX6
The companion special outfits are resetting to their default class outfit if you try to dye them. I'm not sure, maybe this is intentionally?
Also you can 'freeze' certain armor parts as your class outfit. In the beginning of the video you can see that my Oracle wears no armors, but it looks like Scale armor and not the default oracle class armor. That works with all equipment and with all characters. It's easy to reproduce.
Looks like something like a dialogue, a loading zone and similar stuff can cause that the armor "freezes" as your class outfit. After you have the 'new' class outfit look, you can't dye it. You can see in the video, that just a very small part is dyeable now.
Sometimes you can fix this with reloading the game, but tha...