I don't believe in moral relativism either, however, what you believe is moral and just is likely different from what I believe is moral and just. I'm sure I'm right (except where I'm wrong ;-) and I'm sure you believe you're right. If we differ, I believe one of us is wrong.
However, when we come to such an impasse, I'd prefer to acknowledge it, respect one another, and come to a common solution. What common things do opposing groups have in common and how can that be built on?
With the knowledge that I'm stepping into the deep end: many conservatives are convinced that life starts at conception and believe abortion is equivalent to murder. How would you react if your government was legally permitting selective death of a class of people who could not defend themselves?
Another group of people are convinced that separating children from families detained at the border is equivalent to putting them in concentration camps. How would you react if your government was allowing a class of people to be detained without charge?
For whatever reason, it seems many people choose to think one is OK and not the other (sure, there's nuance), but in both cases the outraged party has complete conviction that their view is correct and logical justification for why.
Calling the other group regressive, libtard, or any other demeaning name and showing disgust for them rather than understanding the perspective that their coming from makes it easier to treat the other with disrespect and dismiss their views no matter how sane or logical they may be. Both political cultures have deep contradictions. I see the current political climate as not dissimilar from Cowboys vs. Packers fans. Flip flop on issues all you want, as long as it means winning.
It may not seem like it, but there are very good and culturally healthy reasons to have conservative and progressive viewpoints. I say this outside of a political context.