Many religious organizations in the US openly discriminate against people who are not their religion, from christian charities and businesses requiring staff to sign contracts that state they agree with/are members of the religion, to catholic hospitals openly discriminating against non-catholics based on their own "religious freedom to deny care". One way they can do this is an exemption to discrimination called bona fide occupational qualification suggesting that only certain people can do the job.
In a more broad sense, any private organization with limited membership (signing up vs allowing everyone) can discriminate. For example some country clubs discriminate based on race to this day. One reason for this is that the constitution guarantees "Freedom of Association" which includes the ability to have selective membership.