Now I am confused. Based on the title, I expected /g/admins and /u?exclude_groups=admins to both work for logged-in users, while they don’t work for users who are logged out.
Maybe we are talking about different states of “hidden” on the groups page:
With “hidden,” I meant something like private - visiting /g/admins does lead logged-out users to the oops page. I think you might be thinking of the fact that most users don’t see the default groups on the groups page (except for moderators) because some additional code hides them. But even though the groups are not shown on the groups page, looking at the page of the group is possible for users clicking a link.
The private hidden is what makes the group secret and is the reason why I think it makes sense that the filter on the user directory doesn’t work. It would leak information. The group that is simply not shown, is not secret.