If I were the pastor. I believe I could officiate the funeral. Either a graveside service or at a funeral home.
But NOT at the church. To conduct a queer funeral at the Lord’s house would be profane.
As I read the article, the pastor of the church was not going to be doing the service - the pastor of the church the mother attended was doing the service. They were just using the church because they had so many people coming for the funeral. So if the pastor had allowed the church to be used, he really would have had no control over what was said or what message about homosexuality and gay marriage was being preached across his pulpit. He could have had a case where another minister was preaching that homosexuality was fine and gay marriage acceptable, and his church would have been associated with that heresy.