What's the best we can hope for from society in this case?

There are two answers to give.

Ideally: The influence of fundamentalist/literalist religion declines worldwide. The moderating forces already in existence within the Catholic church, various protestant denominations, etc claim the seats of power, and a reform takes place. LGBT folks get to go to church without having to hunt around to find 'The one with the rainbow flag outside,' without risk of being violently assaulted for something as banal and boring as who they choose to shag. We turn the page on this nasty portion of history and religion is finally something that is good and positive at the exclusion of judgement, fear, anger, hatred and bigotry, and those who exemplify those traits get kicked out of their respective religion, or at the very least they are not allowed to lead.

Practically: The culture war is going to continue. Christianity is going to fracture further. Christians that today ignore the text in favor of feel good 'God is good! All the time! All the time! God is Good!' culture will continue to do so. Christians who take their theology seriously will find a work around so they get to ignore the harsher parts of the text, like they do today. Evangelicals are still breeding like rabbits, and they have enormous political power. Their theology is going to affect the politics of the United States for decades to come, if not centuries. There are just too many of the fuckers, thanks to a lack of fact-based sexual education and direct religious orders to shun birth control and be fruitful and multiply. The best we can hope for with this group is stalemate, cordon off 'Christian territory' in the US and let them have their theocracy, separate from the rest of the world.

If I seem fixated on the LGBT+ thing it's because it's a good weather-vane for the temperament of a church in general. If they think that homosex is an abomination before the eyes of the Lord, they also likely believe that suicides are condemned to the fiery pit.