One of the funny things about the GRA is that it says you become the target sex "for all purposes" on receiving a GRC, then it goes on to list exceptions. Including sports!
I don't remember a religious carveout in the GRA as such - I think the applicable legislation is Schedule 23 of the Equality Act, but (being a 2010 law) it's mostly about protecting churches that don't want to perform same sex marriages.
But I think in terms of religious bodies, and we're talking here about churches that believe only men can be ordained, that it cuts both ways - in that position, you wouldn't want to lay yourself open to litigation from a transman who rocks up wanting to be ordained, but you would also want, in the event of a male priest taking a trip to Malaga Airport, to have the ability to shuffle him out of his position. I can't remember any court cases testing this.
Generally I think the EqA puts far too many pettifogging restrictions on freedom of association, and some sensible rewriting would improve it, but good luck convincing Labour MPs of this.