@FundamentAli, I think you are twisting facts. The song being a befitting theme song, doesn't mean it was written for or in support of gays.
Below is an excerpt from your link.
All in all, i loooove the song.

"They wanted to use it and I told them not to. I am worried about certain songs being used for politics because certain songs are healing songs," Lauper said. "And you don't want anyone to think about politics, you want them to think about their soul and their heart."
But Lauper has had a change of heart herself, given the president's announcement.
"In this moment, with what he said, if there was a theme song [for the moment], it would be 'True Colors,' " she said.

So Cindy is a socketing socket?

copy & paste..........
The song does not specifically talk about God. As I found from Wikipedia, Cohen's original version contains several biblical references, most notably evoking the stories of Samson and traitorous Delilah from the Book of Judges as well as the adulterous King David and Bathsheba: "she cut your hair" and "you saw her bathing on the roof, her beauty in the moonlight overthrew you".
As interpreted by Francis O'Brien:
The first part:This relates to the story of King David who was had an intimate relation with God and was also a great harp player (secret cord/pleased the Lord). The hallelujah at the end of this verse is a happy and spiritual one.
The second part:In this part Cohen relates to the story of David and Bathsheba when David was walking on the roofs he saw her bathing and seduced her ending up committing adultery and lost a lot of influence and weakened his link with god (broken throne). Then we move to the story of Samson who gets his hair cut and loses all his powers, once again, a broken throne. In this verse, the hallelujah is a very sad and desperate one.
The third part:In this part Cohen talks about the ambivalence of love and its effect on your faith. It can be glorious like a flag on a marble arch or it can be cold and broken. And when in heart break you may lose or strengthen your faith, in this case it is strengthened because he still praises the Lord in the end. In this case, the hallelujah is (obviously) cold and broken.
The fourth part:This is an obvious reference to sexuality and that even through an act as disgraceful as sex you can still praise the lord. In this verse the hallelujah can be interpreted as an “orgasmic” one.
The fifth part:In this part, he has found what to believe in and realizes his past errors but he is ready to face the Lord because he now has complete faith. This hallelujah is one of total faith and love for “the Lord”.
Whether Hallelujah is spoken in complete blissful faith or is from broken desperation, its goal is to praise the Lord and it means the same and are all equal.

Alexandra Burke also did her version of Halleluiya very beautifully and she went on to win the 2008 X Factor Final. Link: http://www.youtube.com/watch?v=xaWLsgxDzuw

@FundamentAli, True Colors was the only song in Cyndi Lauper's second album that she DID NOT write.

The song was written by Billy Steinberg about his mother (with Tom Kelly's help).

http://www.songfacts.com/detail.php?id=3101