There are 6 so called 'clobber passages' in the Bible traditionally used to bash LGBT people.
First one is Genesis 19:1-8 - the Sodom and Gomorrah story, which is more about inhospitality and rape (straight) than it is about LGB people.
Then there's Leviticus:
Leviticus 18:22: You shall not lie with a male as with a woman; it is an abomination.
Leviticus 20:13: If a man lies with a male as with a woman, both of them have committed an abomination; they shall be put to death; their blood is upon them.
Romans 1:21-27 is the next one, and pretty much everyone conveniently ignores the 'therefore' at the start of the passage, meaning you also have to read the bit before the 'clobber' passage.
I Corinthians 6:5-11. A list of people who won't get into heaven. If your version of the Bible includes homosexuality in that list, it's a dodgy translation, as the word 'homosexuality' wasn't added in to the Bible until 1947.
I Timothy 1:5-11. Another list of the dodgy lot who have sinned. This one isn't used so much - it's the first five that get quoted all the time.
There are a lot of books you can read about the cultural / historical contexts of the times these passages were written, which indicate the anti-gay meanings put on them in more modern times might not be what was intended at the time (esp the new testament stuff).
Psalm 139 (to me) is a counter to that, especially 'For you created my inmost being; you knit me together in my mother’s womb. I praise you because I am fearfully and wonderfully made'
because I had it drummed into me when I was a kid that God doesn't make mistakes.
Therefore I am neither a mistake nor a 'dreadful sinner'.
The big issue (I think) is whether you think being gay is something that you're born, or if it's a choice. Because whatever people / churches think about that question then determines which path of acceptance (or not) they will go down.
The evangelical lot mostly think it's a choice, or that being gay isn't necesarily a sin, but any same-sex behviour IS a sin - it's the choice to act on it which is the sin. Ironic really, given that the new testament has an lot more about sexual ethics between men and women than it does about two men or two women....yet we're the bad guys.
Paul says he'd prefer that no one married at all, but you never hear that preached from the pulpit. Apparently it's ok for straight people to act on their desires, but not gay people.
A lot of churches (Church in Wales, CofE to a certain extent, Church in Scotland, Quakers, Methodists, for example) don't think being gay is a sin, and that's shaped their responses to LGBT people. The CofE's got a bit of catching up to do, but I think it's getting there - slowly, and some churches are far more accepting than others, but the CofE being a 'broad church' allows for that range of views.
I grew up in an evangelical church (so v anti gay) and now go to a CofE church. The church I go to has (so far) been really welcoming and inclusive, and I've been involved in various things with no issues. I'm not generally 'out' in the congregation (though a far few people know), but I would imagine there'd be some who may not be happy... but that's to be expected in any congregation really. Leadership know and are fine - even with me being married. It really does vary from church to church.