First, I lived in Arkansas for 3 years, and spent time in El Dorado (locally pronounced El Dor-AY-do), and this is deep Bible Belt country. This story is certainly plausible.
Second, I had an ex-BF whose family talked him into entering gay deprogramming in California. He left a good position with Microsoft in Redmond, Washington, sold everything he owned, and was held incommunicado there. I know, because he managed to get some forbidden emails out to me from there. But they finally stopped, and I haven't heard from him in 10 years.
He was "employed" by this group to write software for them, that raised them money. This is how he managed a few emails to me before he was shut down. He told me how he could only go outside the compound with a "chaperone" to make sure he had no forbidden contacts. And he wasn't allowed to be in touch with anyone from his "old life" except his own immediate family.
I knew he was troubled about his sexuality when I met him, at age 36, but I failed to realize how much his family, in another state, was putting pressure on him to change. I still don't understand why he agreed to it, since he didn't share that with me.
The evil of the Christian fundamentalists cannot be understated. They would do this to all of us gays if they could. And the US Republicans are their elected tools, as we see in the news every day.