The GOP has a voter base among the traditional and conservative section of the population and those people are not particularly accepting of the LGBTQ community, yet. Trump did a good thing by including the LGBTQ community but his supporters, at least some or most of them, may think otherwise.
The Republican Party is now the anti-gay party. Their policies include the North Carolina law that forbids transgender people form using the bathroom they identify with as opposed to one associated with their birth. Many homosexuals have condemned the law and businesses are voicing their objections. The NBA was so offended, it moved its All-Star game.
I don't think that the GOP is anti-gay, although they do focus more on traditional values. I think that he party just believes in less government. I've never heard a Republican talk that cares if someone is gay or not, they just want the government to stay out of the whole debate.
While there are plenty of Christians who are Conservative or part of the Republican party it does not mean that the party itself is the anti-gay party. There are a wide variety of people and viewpoints in both parties. Some of whom are Christians/religious people that don't have a problem with homosexuality and secular people who also have no problem with homosexuality. Just like there are probably Democrats/Liberals who don't like homosexuality.