This is a great way to prove the point of the concept. As a moderate, I could choose to say, "No, fuck you. You're indoctrinating kids to think they have a severe mental illness and that the only cure is hormone therapy and reconstructive surgery! I won't be civil with you!"
You don't compromise with people you agree with. You compromise with people you disagree with. The minute you think compromise is out the door, that's when we might as well duke this out in the streets, because that is the only option you are leaving your opponents. I'd prefer compromise.
It's easy to believe you have nothing in common with your political rivals. Especially when all you see reported are the opinions of the worst of the worst. Fortunate, we have a lot more in common than not. All it takes is for both sides to sit down and start talking in good faith. That's how Daryl Davis, a black man, deradicalized over 200 KKK members. If you think you have less in common with the average conservative than a black man with the KKK, you're mistaken.
Stop focusing on the news and soundbites from politicians who are trying to rile up their base. Stop focusing on what angry people say online when they are anonymous. Sit down, in person, with someone who holds beliefs you disagree with, and have a genuine conversation. Don't listen to them waiting to disagree, listen to them with the goal of understanding why they believe what they believe, and humanizing them. That's how you live together in a country full of people with different opinions and beliefs. That's how you get concessions and get people to understand you in return. You talk with them, not at them.