Background - been with DH for 25 years, married for 20. Two teenage DDs and a grown-up DSD. Met when we were quite young, in our early 40's now.
Our relationship has always been fairly stable, we've been through some ups and downs, almost split about 10 years ago but managed to come back and have been happy together since.
We've always fairly similar left-wing political views. And have managed to mostly agree on the important things and the little things seem unimportant.
I'm fairly political minded, it's always been a big part of who I am, I've always been opinionated and loud. 
We met when I was 16 and I was as opinionated about my views then as I am now. What I believe in hasn't changed, I've always been a feminist and I'm loud about women's rights. They're important to me and form a large part of my personality. I've also been an atheist since I was about 12.
DH has always been religious on a relatively small scale. He's never really settled on a religion, trying different ones on for size over the years. Although always Christian religions. We've always managed to somehow find a common ground and create a balance between his beliefs and mine.
We brought the kids up as non believers, although they did attend a primary school that leaned towards CofE. Now as teens dd1 (16) is a complete atheist and dd2 (13) believes in god but doesn't follow any religion.
In the past year or so DH's religious beliefs have slowly gotten more and more "conservative" I suppose. To the point where now he's against abortion, gay people (! 
) birth control etc. We've gotten into some major arguments in the past year where I've seriously thought about whether I can continue to be with him. So far we've managed to plod along by avoiding all these subjects.
Sometimes he'll go into preach mode with the kids, DD1 shuts him down completely will walk out of the room and call him quite a few names that I won't repeat. DD2 will listen more and try to debate but mostly rolls her eyes.
It came to a head on Friday morning, we were walking the dog in the park just having general chit chat when I brought up that case that's been in the news recently about the mum in the US who complained to her son's college because the women wore leggings. I brought it up in a rather jovial manner, my view being the woman is obviously being ridiculous. I never expected that he would agree with her! WTF!
We ended up getting into a massive argument in the park, at one point another (female) dog walker who'd been walking not far from us commented, (on the obvious ridiculousness of it all) and then wished me luck! I said to him that I couldn't believe a man with 3 daughters could hold the belief that women shouldn't wear leggings!
I threw all manner of counterarguments at him, including his hypocrisy about birth control considering he's had a bloody vasectomy!
He watches a lot of bible videos on youtube, you know the type American preacher, creationism (which he now believes in ), etc. Which is obviously fueling this. This kind of extreme thinking isn't necessarily new before we got married he considered becoming a Mormon. He decided against it when I told him I wasn't converting, which was a requirement as we were "living in sin" at the time.
Now I find myself at a point. How do I carry on a marriage with a man whose views are polar opposite to mine? If he'd had these views when I met him 25 years ago I wouldn't have looked twice at him, let alone started a relationship and had kids with him.
We're on talking terms at the moment just to be functional. This morning he tried to initiate sex, but I pushed him away. Although I love him and fancy him, I'm repulsed by his views. How can I have sex with a man who thinks women hold some responsibility in the way men react to them?
As far as the type of person he is, he's the last person you would expect to hold views like this. He's nice, gentle, easy going, rarely raises his voice. Fairly low key. Which is why I think I've been able to gloss over his views for the past year or so. But now, when they're just staring me in the face I feel like a bloody traitor if I was to sleep with him again or carry on this marriage. It's going against all my beliefs.
As far as the practical side of things goes, if we did split up we would have to stay living together. Atm we're on benefits, dd1 has Autism and I'm her carer, he was made redundant last year and hasn't been able to find a job so far, and even then he's only ever earned minimum wage. So financially splitting up really isn't an option. He doesn't have any family he could move in with, his parents are dead and he doesn't speak to his brother.
I don't know what the fuck to do. 