The custom user fields do show up on the user profile page now - not sure when that was implemented. But it does seem to be a bit halfbaked and is not especially configurable. And do not yet display on user cards.
What I’d like to display on user cards and user profiles is organizational affiliation as a link. But putting that HTML in the text field doesn’t work as expected. It includes the field title and the HTML is exposed - see screenshot.
What if we enabled the contents of a custom user field to be used as title? Or as a badge?
