I think the biggest obstacle is probably that flagging it requires asking for information on it. There's a lot of icky history about quotas to prevent there be

I think the biggest obstacle is probably that flagging it requires asking for information on it. There's a lot of icky history about quotas to prevent there being "too many" Jews in a particular organization, for example. If you ask what a prospective hire's religion/congregation/parish/etc. is, you may say it's to prevent a conflict of interest, but it looks bad, and probably invites as much legal trouble as not monitoring it, if not more.