Except that religious exemption applies only to discrimination on the basis of sex. This claim is about discrimination on the basis of marital status and/or sexual orientation. If Parliament had wanted religious groups to be able to discriminate for those reasons, they would have said so. They didn't, so its illegal.
But my pleasure at their discomfort aside, the fundamental fact is that the Anglican church is a bigot organisation, and no decent person should have anything to do with them anyway.
Updated: Graeme Edgeler has pointed out that this isn't a question of employment, but one of a "qualifying body". But again while there is an exemption for organised religions, it applies only to discrimination on the basis of sex. Similarly, there is an exemption allowing discrimination on the basis of religious belief for religious employment (s28(2)(b)(i)), but that doesn't permit discrimination on the basis of marital status or sexual orientation either.