Just trying to make the point if you allow religious headgear for one group, it would have to be allowed for all, even though I know there’s a world of difference between a turban and a yamaka. Especially as far as fitting under a beret!
The correct answer here is that there are no other religions with such an extreme requirement in terms of headgear. If you’ve got the Sikhs covered (well, if you let them cover themselves as they please) then you’ve got no worries about other cases.