The American Psychological Association apparently decided
not to drop its exemption for religious schools (giving it the reverse policy of the AEA) in 2002. This
site argues that the repeal of the APA exemption was sought by gay groups which "feared that the exemption would result in anti-gay discrimination." I'm not sure about the
sponsor of that site - I don't know enough about the politics of the psychology field - but the report of the APA action seems straightforward.