Rethink what you mean by "what are we supposed to do?"

You're not going to convince them, you're not going to change their mind, you're not going to find the one flaw that shakes them from their delusion. Because conservativism is not founded on principles. A conservative is a narcissist, and should be treated as such. Ignore their tantrums, protect yourself and your interests, set boundaries and stick to them. Their arguments are flotsam flung from whatever position they think will help them most. Ignore them, it's all bullshit. Their priorities are lines in the sand drawn around where they stand. Ignore them and do what you know to be right. Do not compromise, do not waver, do not negotiate. That's a losing strategy every time, because their appetite for self interest is never sated. Their lust for power will grow with every inch you cede.

They are not an enemy to be vanquished with thoughtful debate, they are an obstacle to be overcome with tireless devotion to doing good.

Also do not seek revenge. Do not say "they have hurt me, I must hurt them." The conservative craves your attention and will feel validated by your wrath. "See?" they will say, "I knew you were as bad as me. You criticize me, but we are the same." Forgive them, and move on with your life. A conservative may learn that being kinder to others benefits themselves. This doesn't mean they are cured of their conservativism, merely that they have adapted to the new normal where you aren't playing their games. They will pretend they were on your side all along. They will claim to have been confused or lost or fooled, but they are merely deflecting blame for their willful ignorance. You can enjoy the time they spend feigning compassion, but be vigilant against the selfish gremlin inside waiting to latch onto any advantage they can find for themselves. If you give a mouse a cookie...