If we really want progress, we should recognize a much more fundamental and deep divide than conservative versus liberal: those who use logical fallacies in argument and those who don’t. Liberalism and conservatism are the poles of constructive debate; as opponents acting in good faith, we can still be allies in reason.
What makes politics so divisive and counterproductive is not the divide between liberals and conservatives; it’s the unacknowledged divide between those who demonstrate a respect for logic and those who don’t. Note I said “demonstrate respect” for logic; failing to demonstrate respect is not the same as holding contempt. We did not evolve to practice and value logic. In the absence of training, we tend to use logic only to get what we want.
If you really want to make a better world rather than advance your own selfish agenda by getting your tribe to support your personal, narrow grievances, then learn about logical fallacies, reject them, and pressure your friends — gently — to do the same. I’m not wrong about this.
I may be biased, but the fallacies you should learn and reject first are Ad Hominem (often carried out implicitly in a condescending tone), Appeal to Authority, Strawman, Slippery Slope, and the Naturalistic and Appeal to Nature fallacies. (And, I suppose, Middle Ground; I’m not advocating for Middle Ground here at all. Some concepts are simply correct and others wrong, even if they’re popularly set against each other, like the theory of evolution versus myth-literal creationism. Aw, heck, learn all the fallacies.)
Unfortunately, entire social movements have been and still are propped up by the consistent use of logical fallacy in argument.