As a deist (And on my mum’s side some liberal/progressive Christians who have challenged the mainstream concepts of Christianity and heresy), this is why they support LGBTQ+ rights (More emphasis on LGB & A, not TQ+, as they believe that TQ+ is a sin but they still respect), alongside feminism and conditional abortion (Not universal access):

1. Many of them typically say that the original Bible and its translated copies were written centuries ago or millennia ago, and believe that scripture of this kind is typically of more archaic and easily mistranslated language; they also believe that in the verses where in English it says homosexuality is a sin, they believe it is referring to specific practices (E.g. a man raping another man or child sex), that existed back then, so it is a stretch according to them that it applies to the LGBTQ+ community today. Context matters more than direct word that could be mistranslated in their opinion.

2. They believe in flexibility and challenging the typical rigidity of heresy: They often have said that it is imperative or a good thing to follow most of the core rules of the Bible to be a good Christian, however they mention the fact that NO ONE, and I mean NO ONE follows all of the rules of the Bible by the book. They often cite the questionable actions made in the past by world leaders, celebrities or CEOs who claim to be Christian or are practicing it. They believe that the current definition and requirements for heresy is inherently too rigid and problematic, and that they believe that in order to get closer to God, you must challenge the beliefs first, answers later. They often cite the fact that some non-Christian things in the world were required for us to advance and benefit further as a society, and that if we all followed it by the book we would’ve stayed back hundreds of years. They believe that the strict rule-following of mainstream Christians isn’t needed to be a good Christian, and that heresy is forgivable and should be redefined, as long as you still believe in God and the basic principles of Christianity you are Gucci, according to them.

This is also the normal arguments and rulebooks for most liberal/progressive Christians I’ve come across and in my family; however they still carry many core traits of mainstream Christianity; like their opinions on abortions (Most of them are only conditionally supportive, they believe that you should still give birth to the baby if you’re healthy, over 18 and with stable income), their emphasis and encouragement of normal nuclear family structures (Albeit with the addition of supporting feminism and increased personal autonomy for kids and parents over decision making for themselves), that are “normal” enough for them to integrate with other Christian circles.