As you know, this is a difficult question. How SHOULD society react? With compassion and firm boundaries. (addressed in other posts) How DOES society/human nature react? Pursuant to our own self-interest and fears, as usual.
It is difficult if not impossible to enact "love the sinner, hate the sin" when the sinner immediately rejects your efforts to reach out as soon as they realize you don't condone their sin. (For instance, I love my gay friends but utterly reject gay "marriage." For them, to reject gay marriage is the equivalent of rejecting them.)
This is a serious obstacle. Ideas on how to overcome it? I also think that the labeled person has to be open to possibility that someone might love them but reject their sin. How many LGBTQ+s do you know that are?
I do believe the fires of division have been stoked to quite a blaze in recent years.
How SHOULD society react? With compassion and firm boundaries.
Again, the community appears to be divided primarily between those who by virtue of the circumstances of their birth have no immediate choice in the matter and those who chose their behavior. So each part of your answer fits nicely into one or the other of those two groups.
There appears to be at least two models of therapy. The key for society then, is to identify which of the two groups a particular individual is a part of. With a careful approach that should not be difficult.
When an individual "immediately rejects your efforts to reach out as soon as they realize you don't condone their sin", it is probably wisest to not lead with biblical verses.
I endorse setting firm boundaries for the "choice" segment. Unfortunately, society is proceeding from a weak position in that regard due to the many liberal, indeed anti-MAGA forces that have caused it to embrace among other things, same-sex marriage.