Depends on church, I recently visited the babtism of a Lesbian couples' child featuring readings by a trans lay-minister. This was CoE, rather than any 'rainbow church'.

It's true that almost every mainline Church denies the right of gays and poly's to marry as they would wish. Beyond that single sacrement however there's no need for exclusion. Many congregations are still full of assholes, absolutely, but you'd be surprised how often the views of the Church body diverge from talking heads like Calvin Robinson.

Trans-rights are an odd-space. There isn't actually anything in the bible explicitly denying trans ontology (at least for binary trans people), so again it's a matter of specific bigotry rather than institutional bigotry.