How do the political Left and Right view each other?

If you haven't watched it yet, you can at least read the summary of the study outcomes by NYU social psychologist Jonathan Haidt.

Note for the sake of judging biases that I consider myself a traditional liberal, leaning left. I find myself absolutely appalled at the belief systems of the "social justice" left (aka, regressive left) as well as the bigoted right, mostly because I've spend time and effort into understanding their arguments.

The fundamentally problem is that both are making the same mistakes in reasoning. They both define people by identity groups and live by the fallacy of division, meaning they think that properties of the group apply to the individuals ("blacks are criminals", "whites/men are privileged"), and hence you can treat individuals by their group and not their individual merit.

They both often combine this with base rate errors. For instance, the bigoted right confuse "terrorists tend to be Muslims" (which is true) with "Muslims tend to be terrorists" (which is not even close to being true). The social justice left confuses the statement "privileged people tend to be white males" (which is true) with "white males tend to be privileged" (which is not even close to being true). The inversion becomes clear when you apply it to a non-emotional situation: "crows tend to be birds" (100% are) clearly does not mean that "birds tend to be crows" (only a tiny fraction of 1% are).

They fall into in-group/out-group behaviours which is best understood via Realistic Conflict Theory as demonstrated in the Robber's Cave Experiment and Jane Elliot's famous classroom experiment. The principle has been repeated thousands of times and is well understood as an evolutionary adaptation based on our tribal past. We humans can be made to fundamentally hate each other with vitriol and violence purely based on a couple of simple steps:

1. Divide people into groups. They can be random (as in Robbers Cave Experiment) or arbitrary (as in eye colour of Elliot's experiment), or a myriad of other divisors (skin color, sports teams, political leanings, nationality, gender).

2. Put the groups in conflict with each other, either by sparking the conflict with competition (rewards, punishments, attention, moral status) or inter-group insults ("criminals", "privileged", "weak", "fascist", "communist", "immoral", ...)

What results is increasing extremism between groups. Hatred is created out of nothingness and can grow to define self-reinforcing cultures about what "we" are like and what "they" are like, obviously exaggerating both, and dismissing the criticisms of "them" because they are clearly wrong.

This is what political affiliations do (left/right, Republican/Democrat, liberal/conservative). This is what bigotry does (white>black, men>women, hetero>homo, cis>trans). This is what identity politics and the "progressive stack" does (black>white, women>men, homo>hetero, trans>cis). This is why they often end up with the same oppressive policies, only reversed, such as the idea it's ok to fire somebody because of their skin colour and hire somebody of the "correct" skin colour. The only real difference is the hierarchical order they put the different groups. Right-wing bigots put the majority/dominant on top and more fringe groups at the bottom; left-wing regressives do the inverse of this.

Realistic Conflict Theory provides the solution though, which was stage 3 of the Robber's Cave Experiment. Stop treating people by their groups, start treating people by individual merit, and focus on solving social issues as common rules that apply to everybody equally.

For example, instead of dealing with "black poverty" and "white poverty", you deal with poverty regardless of color. If there is a statistical difference between groups, then by addressing the common interest of eliminating poverty you will inherently help the statistically worse off group anyway as a result, and in the correct exact proportion.

There's a name for that approach; we've always called it liberalism (though it overlaps with modern libertarianism as well, which differs from liberalism in other contexts). We judge people not by the colour of their skin, but by the content of the character.