I think it is a function used for shaming.
Agree, shaming rather than to use a more authoritarian approach and instead to outlaw some expressions of free speech.
It's ironic given that anti-shaming is also a thing in the current culture.
Shaming is used for all sorts of purposes, generally to get people to conform to something.
But there is a huge difference in:
1. Shaming a person for being LGBT
2. Shaming a person for discriminating against people who are LGBT.
For item 1 a person is who they are. Their being who they are isn't in order to be mean to others in society, it isn't to pick on groups of people in a diverse society.
For item 2 this is intended to attack and hurt other members of society.
So people who are "against shaming" are typically against hate or discrimination of groups of people in society.
And this means that they will be typically for "shaming" of people who discriminate or say things that are hurtful or mean to groups of people in society.
"shame" isn't the operative word, the operative word is "discrimination"
"Shame" is a tool that both sides can use.
Nonetheless, political correctness is a form of shaming for the purposes of influence and control.
Of specific contexts, yes, to try and get society to support and respect (or at least tolerate) diversity and their fellow society members. Well, at least publicly, You can't force a person to like LGBT people but hopefully you can convince them to not express derogatory or hurtful/hateful expressions towards this group in public.