Ya, so political correctness is an issue. For example, Christians are treated very poorly by atheists and other secularists. It is perfectly okay to be a dick to Christians (it is, btw), because of their "history and power" or some ****. Acting the same way toward Muslims will make you the enemy of all that is free and decent. Yiannopoulos sees this, so he goes on Twitter and starts trashing Muslims or women or transgendered people, because joining the chorus trashing Christians and whites is no fun.
You mean his opponents started doxxing Republicans and conservatives in response to Milo being invited to speak, like this time
https://www.washingtontimes.com/news/2017/jan/11/milo-yiannopoulos-invite-sparks-malicious-attack-o/
And of course they justified it by making the usual claim about how their victims are subhuman bigots anyway. I am not familiar with every doxxing incident, and I know the alt-right engage it all the time (both sides do). So I don't know of any incidents where Milo himself doxxed someone.
Again, their point is that everyone should be able to speak their mind, without fearing for their lives or careers because it goes against what you referred to as the liberal bubble. There is nothing shocking or Hitlerisque about opposing same-sex marriage. Someone who donated to a "traditional marriage" cause shouldn't have a million people harassing their employer until they are fired. It is a corruption of liberalism and it should not be tolerated. We shouldn't have rallies that try to force universities to drop Western Civ courses. As a liberal, I find this **** 1000 times more offensive than some idiot talking about establishing a whites-only nation.