Exactly, Brandi. There was also a RC service in London that ministered to the LGBT community and friends, but was shut down earlier this year because it was sending the 'wrong' message.
Your 'own branch' already exists, interestingly. The Reformed Catholic Church exists over here in the UK (and I think Europe to some degree, maybe further afield). Its (one of its?) archbishop is a openly gay, female, queer theologian.
The homophobia. however, is not just a Catholic preoccupation. It also exists through a great many evangelical churches, too. The trouble is that only the RC church presents an apparently unified front.
The 'lacking faith' thing, which is real, is nastily condemnatory.
The 'positive thought' thing may well be true. If I remember my experiments from busines studies correctly, factory workers improved productivity when played different music, classical I think, which was heralded as a breakthrough. A following study then found that productivity was also improved when the workers were _told_ they were going to have a different mix, but weren't. It seems that it was just the being thought about that worked.
And that may well be the issue with the so-called 'justifications that prayer works' experiments - knowing you are being thought about may give a significant psychological boost.
ha ha pot meet kettle. Now that's rich.