The branding that they are love and everyone who disagrees is hate that demonizes anyone who disagrees. Whether it is saying the best place to raise a child is a married heterosexual couple to saying we shouldn't let children too young to drive decide they are the opposite sex, express these views and you're smeared & called evil. The name calling is the default response and sometimes escalates to hate mobs trying to cost you your job and death threats.
The authoritarian left says we just want to live our lives, stay out of the bedroom. A church says our doctrine is X, we won't change, next comes the hate mob and death threats.
A number of private religious schools, including one near us, were targeted for enrollment of a homosexual's child in contradiction to their policies. The schools want to teach traditional marriage and not create personal conflict, so they say no, we won't take the kids. The authoritarians want to enroll the children and force conservatives to change - disrespecting the rights of others to have their own views and institutions; it's like a Christian showing up at a mosque and demanding they stop teaching Islam.
The school near us declined the child. National headlines about the bigoted school. The death threats to the teachers, administrators and staff went on for months and didn't even make local news.
I cannot understand the thought bubble where someone could threaten to burn down a school with 200 pre-K-8th grade children inside to kill the haters could be "in the name of love". But when you have good branding, threatening mass murder is apparently OK.
Then there's the hypocrisy; a Muslim shoots up a night club per the Koran's mandate to kill homosexuals and the teachings of his Imam ... and Christians are blamed for the "atmosphere of hate", while people who don't want to make a blasphemous wedding cake are lumped in with Muslims who execute homosexuals. (Note: Iran does it it as do ISIS and Saudi Arabia).
It is immoral moral equivalence, but when you say you're on the love and tolerance side, you can refuse to tolerate others views and be as hateful as the Muslims who are actually killing homosexuals.
When your desire to live per your principles is attacked as evil, you get threatened by those who say they are the tolerant and then attacked by them when their members were killed by a totally different religious group ... it is hard to put up with them.