There are many Christian churches that don't discriminate against gay people, and there are even churches with predominantly gay congregations. Being Christian doesn't necessarily include persecuting gay people.
For example, if you check the main page of Metropolitan Community Churches, they say their focus is to "Do justice, show kindness, and live humbly with God. (Micah 6:8)". MCC churches can be found in most metropolitan areas in the US, and around the world. I've been to same sex weddings at MCC churches. They don't discriminate or judge, which to me seems a very Christian path to follow.
As to why a gay person would want to be Christian, well, why would anyone? The reasons don't change just because of a person's sexual orientation.