They're protected in the US, and liberal democracies (though some far right countries in Europe, like Hungary, are trying to reverse these protections). And no one is asking you, personally, to support their political agendas. Just to understand why some governments (or embassies) show solidarity. With LGBT+, with people suffering gender based violence, with people suffering caste discrimination, or not enjoying freedom of religion. And the same reason they don't support mainstream issues which are uncontroversial.
Actually, LGBTQ and black activists have gotten professors fired from Universities for
not supporting their agendas.
Bret Weinstein and his wife were forced to resign from Evergreen State U, because
they opposed a program the administration came up with, that all white students
needed to stay home for a day while, blacks and people of color would attend classes.
This was discrimination at it's peak and when Bret Weinstein and his wife spoke out against it, radical leftists went to their classes and talks, yelling at them and shutting
them down. There were also riots to have them fired. They chose to resign instead.
In my dioceses, two activists claimed they were discriminated against when they tried to buy Church property that was for sale. They sued the dioceses and of course it made it into the front page of the newspapers. However, the dioceses had no idea who was trying to buy the property, as it was a real-estate agent handling the sale. Turns out, the two male activists, had no money to buy the property, but used the sale as a political stunt
to discredit the dioceses. They ended up dropping the lawsuit as they saw how they were going to lose.
In other areas of the nation, same-sex couples tried to sue ministers for refusing to marry them.
Average Americans are finally starting to push back and not accept LGBTQ nonsense.