I think you've run away with a few generalisations and got carried away with hyperbole here. Trans rights (and what they mean for society) are still very much being debated. The vast majority of liberals, including myself will have no problem facilitating the emergence of a compassionate society. I am confident of that because most people want other people to do well.
Where the disconnect is happening is the hot button issues.... primarily, pronouns, sporting events and bathrooms - the ones being discussed most and debated most, affect the least number of people. Whether or not trans-people have rights is not the same as whether this trans-person should be allowed to compete at the Olympics.... this has led to a conflation of genuine trans-hatred with anyone who says 'no' or 'hang on a second' to a trans-demand.
If I wrote a story in which a young Spanish woman showed up, heavily pregnant at an American hospital... where the staff immediately helped to deliver her baby - and afterwards, she complained vociferously that nobody spoke to her in Spanish, that woman would be 'entitled'. That's the same thing here.
Equality doesn't always have to be nice... equality means you get treated the same as everyone else. In this case, this guy overstepped the mark. He wanted the world to immediately accommodate his very specific need and he kicked off when that didn't happen. As the article makes clear, I've got no problems with a guy showing up at a hospital pregnant, I've got no problem getting my head around this at all, but I don't have to endorse it. You can try and equate that with the worst kind of genocide if you want - but I think that's disingenous.
And worse, I think it's dangerous. I think activists who overreach with their rhetoric do far more harm than good to trans people in the long run. Something I debated (ish) with James Finn a long time ago - over the inclusion of a trans-friendly book on the curriculum.