Even if you cite religious demographics, it still doesn't mean that all of them are homophobic bigots, it also means that part of them are gay even among those who hide it. While people with same sex attraction are among them, so are pedophiles, although they're not mutually inclusive. If it's a patriarchy, it actually means predator havens, women subjugation, victim blaming... meaning more rape, pedophilia, unwanted pregnancies and secret abortions (or even infanticide) than in cultures with more advanced rights.
Since people do not decide their orientation, many Muslims are gay just like in any other group. Many who have the opportunity live in countries where they face less persecution. If you really believe that gay people don't exist around you, you're just blind, like me when I was young and raised in a cult. As part of the doctrine was the disdain of homosexuality but as a hetero in a culture where gays hid their orientation, they seemed to be like a legend to me.
Afterall, the Jehovah's Witnesses are also superstitious and believe in a lot of nonsense, why would this be different? But I learned that they really exist and often it took years for me to learn that some people I knew for a long time are. Their personal life is not my business and it doesn't change anything.