As foreigner who have followed US politics for over 20 years and lived in the country, I would say neither American liberals nor American conservatives get each other very well.
I think you with this piece have also demonstrated that you don't really get the American left and right that well either.
You take the more extreme rethoric, often meant more as a slogan than any kind of deep analysis or reflection to analyze how your political opponents see things. Ironically you don't apply these same principles to your own side.
When American liberals talk about Gun control, I very often see American conservatives react as if they said: We are going to take away all your guns. Conservatives often are unable to pick up the difference between stricter regulation and taking away guns. But really a lot of this is not so much about misunderstand as it is about the fact that American liberals and conservatives simpl don't trust each other. Trust is in general something I notice is in very low supply in American society. Americans tend to think the worst of each other.
If somebody talks about gun regulation, they think it is simply a plot to trick them into going down a path towards a complete ban.
As for gun violence, you mistake rethoric with beliefs. I think most liberals grasp that gun violence is about a lot more than the guns themselves. However liberals know that all serious research on the topic shows clearly that gun regulations is the primary reason there is so much higher gun related deaths in America than in comparable countries.
Here conservatives Americans are as we can easily see abroad closign their eyes to science as they have with global warming, COIVD19 and many other topics where reality does not agree with their ideological convictions.
Anti-science also exist in some measure on the left, but I would say that is often more rooted in distrust of government. E.g. the left is quite opposed to nuclear power even if it is quite safe. Yet this distrust developed in large part due to the inability of past governments to be transparent and open about nuclear problemes: waste, radiation, safety etc.
It is hard to make the same case for why conservatives should be skeptical of the theory of evolution, man made climate change, COIVD19 etc. There is to my knowledge no history of e.g. governments inventing fake viruses and creating a global scare. If anything the opposite is true: Government have a history of downplaying these kinds of events.