The problem, and challenge for us gays, is that conservative protestants believe there are just a few "chosen" to enter God's kingdom. Add to that, the question "who are we to tell God what to do or who to accept?" is also prevalent.
You've hit the nail on the head with your observation that "gay" isn't something one cures - hence the abysmal, if not non-existent track record for conversion therapy programs.
One clue that God doesn't have an issue with gays is God doesn't change them when they ask - and many, many gay Christians have asked!
Thanks for pointing out the hypocrisy of the statement "Doesn't judge..." and for an important message!