The Pew Research Center conducted a survey on the correlation between religious (specifically Christian) belief and acceptance of trans people, and the results are entire predictable: the more pious someone is, the less likely they are to accept their fellow trans man or woman. White evangelicals are particularly closed-minded on the issue.

63% of Christians, including 51% of Catholics and 84% of evangelicals, believe gender is determined at birth and immovable, versus only 37% of religiously unaffiliated people, including 29% of atheists and agnostics. (Of course, that number is still far too high to be ideal.)

Meanwhile, the majority of Christians (including 84% of evangelicals) think US society has gone too far or just far enough in accepting trans people (read: treating them like people deserving of the same rights and protections as everyone else). Conversely, 57% of religious ‘nones’, including 65% of atheists, think there’s still a ways to go.
This last chart is also unsurprising, and it helps explain the previous ones:

It’s long been clear that by far the best way for people to learn to accept other minority groups is to be exposed to them, especially if a friend or family member is part of one. Nothing changes a bigot’s mind about what trans folk (or gays, or Muslims, or atheists, etc.) are like faster than personally knowing one, especially if they interact on a day-to-day basis. It’s hard to swallow the “transgenders want to rape kids in bathrooms” spiel when you can see that trans people are just regular people trying to get by like anyone else.
There’s also a bit of a self-fulfilling cycle going on – the more people meet trans folk, the more they come to accept them, which in turn means they’re less likely to avoid trans people in the future. The reverse also holds: the fewer people of different minorities you meet, the easier it is to believe hateful and divisive nonsense about them, which makes you less likely to want to interact with them. This is, of course, a large part of why urban areas, where tons of people from various backgrounds live in proximity, are typically far more liberal, whereas more rural regions where it’s easier to remain insular tend to lean conservative. It’s basic tribalism at work.
(via Friendly Atheist)
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