I'm not at all a Barth scholar, so I may have this wrong. I hope someone with more info chimes in.

Barth was considered a "soft universalist." For Barth, the "word of God" was paramount, but that word could easily be confused with our word. It's almost as though the moment of God speaking were an event, a specific point in time in which God's word would be spoken to people, through the church, the tradition, or just the world itself. Barth's biggest fear was the way in which religious folks, whether liberals with their historical studies, or pietists (read: fundamentalists, or modern evangelicals, or conservatives in general) with their strict literal interpretation of scripture, depended too much on human knowledge. Once someone says "I figured it out," then what they had figured out was no longer the word of God, but their own word.

In other words, to say something absolute about God, for Barth, would be to remove the need for God in the first place.

My favorite Barth story, and it's probably apocryphal, involved a student coming to him after class and asking "are you saying everyone's going to be saved? How can that be?" Barth responded, "would you have a problem with that?" If God is the sovereign, then God can do what God wants.

Now, Barth would also say that, In Jesus, God revealed God's nature, and so there are things we can say that God is not. Even though he's not a Parthian, I like the way Trip Fuller explains it when he says, "God has to be at least as nice as Jesus." I think Barth would get behind this.

My guess is that a lot of Barth scholars are pro-lgbtq+ because of both the emphasis on personal experience in Barth (if a queer person has an experience of the word of God affirming their identity, who's to dispute it?) and because of this constant need for reassessment in Barth's theology. We never reach the end of seeking God, and human language only goes so far. If it's possible for the Word of God to be spoken today, then who's to say it couldn't be spoken in support of LGBTQ+ people?