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The answer to both questions is "no". The Church of Scientology is not active in LGBT issues and never has been active in those issues.A claim to the contrary is spread anonymously by members of the "Anonymous movement" who since day one of their criminal activities against the Church of Scientology have tried to gain the support of LGBT community leaders by inventing stories that the Church of Scientology would try to "cure" homosexuality or would treat homosexuals differently. These lies don't hold water and the real makers in the LGBT have proven to be clever enough not to fall for lies of anonymous hate-mongers.
Here is what Scientology has to say about sex:
In 1967 Scientology founder L. Ron Hubbard issued a policy which reads, in part, "It has never been any part of my plans to regulate or to attempt to regulate the private lives of individuals. Whenever this has occurred, it has not resulted in any improved condition... Therefore all former rules, regulations and polices relating to the sexual activities of Scientologists are canceled."
Hubbard later released a book about ethical behavior that was silent on the subject of homosexuality, and offered a gender-neutral ethical guidelines about being faithful to one's partner and avoiding promiscuity (more information about "What does Scientology say about sex and sexual relations?" can be found on the internet, e.g. here).
The Church of Scientology is supporting one of the biggest human rights education campaigns on earth. Thousands of Scientology volunteers fight discrimination and unequal treatment every single day and have worked together on human rights issues with the United Nations, the OSCE, the IHF and other international organizations to create a future for all.
The inventions and outright lies of some "anonymous" cowards show their view on "human rights" and their understanding of fair and equal treatment: none.

