That second point is true, but what he said was that there's no reason Christianity would inherently have more bigots than any other religion. People understand religion in different ways, but that's not the core religion's fault. A lot of people take some Islamic teachings in a way that most would consider wrong, but that doesn't make the actual teaching wrong.
But there is no such thing as a "core religion" in real life. There are only religions. We call Mormons and Roman Catholics and Southern Baptists and Pentecostals all Christians because they are historically connected and have some beliefs in common, but they're very different, and what matters is how each community plays out on the ground. The interpretation
is the religion, for each different Christian community. There is no "core" to be found in the Bible, or in the teachings of Jesus, or anywhere else, that forms the true heart of all of those forms of Christianity.
In fact, if we were to take their actual beliefs and practices and see what they have in common, we would have to conclude that the fear and hatred of homosexuals is, in fact, one of the core beliefs of Christianity. It's certainly one of the aspects of Christianity that is most actively promoted by Christians, and one of the aspects that they feel most strongly about imposing on society in general. Even relatively liberal Christians who think we should have equal rights under the law manage to content themselves with rigid discrimination within the church.