I have strong feelings about this, so please don’t read this as anger but as passion for the Word of God.
I can't really say that I agree with your comment "it doesn't really work to simplify the discussion to "just read the Bible" because people on both sides are reading the Bible, and, with integrity, they are arriving at different conclusions."
As far a homosexuality is concerned, the Bible is very clear that it is wrong ("abomination" and "wicked" are a few words used to describe it). The people who support homosexuality have to go through some amazing intellectual gymnastics to come to the conclusion that the Bible/God says it is not a sin and a lifestyle that should be encouraged by the Christian church. The people are doing their best to fit God into their own beliefs about what is right and wrong. So are they reading the Bible with integrity? No, they are doing their best to invent loopholes that allows them to have guilty free beliefs or lifestyles.
The ELCA can not say the homosexuality is a sin now. If they did, could they honestly encourage people to continue doing it? No. It is a dangerous thing to claim something is good that God has declared a sin. I do not think a tornado hits the building the ELCA is in, at the time of the scheduled vote on homosexuality if God is pleased with what the ELCA is doing.
The fact is this is not just about homosexuality. The ELCA has been teaching for years, in essence, that the bible is not true. They claim Jesus did not say what is in the Bible. They say there is no prophecy in the bible. They think the creation account did not truly happen. When you can make these claims you, as a denomination can elevate your our beliefs above God’s word. Sounds like they believe God was not involved in the writing of the Bible.
Also, if they can say Jesus didn't say what the bible says he said, aren't they in fact saying the authors are lying? The authors say, "Jesus said." The ELCA thinks they are pretty smart if they think they know better then Jesus' friends. They know more about if Jesus said something 2000 years after it happened then those that were there?
If the Biblical authors are lying about this and about prophecy being real (the authors say it is prophecy about things to come) isn't the ELCA truly saying the Bible is a book of lies? And if God inspired it, then God is a liar.
We can not be scared to stand on the Word of God. If people leave, so be it.
It is time to leave a denomination that has left God long ago.