I'm interested to see any studies you can find on this topic. Here are some studies that I have:

Equalitarianism: A Source of Liberal Bias [1] - in study 6, liberals were shown to be ...pretty racist.

You claimed the Right believes fake news. I wont dispute that. I'll just reply that there's a lot of that going around. Here are some examples that debunk fake news you yourself might fervently believe:

Girls Who Code: A Randomized Field Experiment on Gender-Based Hiring Discrimination [2] - leftists tend to believe that women are discriminated against in STEM.

An Empirical Analysis of Racial Differences in Police Use of Force [3] - debunks the common belief, on the Left, that police are more likely to shoot people of color. Quote: "we find, after controlling for suspect demographics, ocer demographics, encounter characteristics, suspect weapon and year fixed effects, that blacks are 27.4 percent less likely to be shot at by police relative to non-black, non-Hispanics"

[1] https://www.researchgate.net/publication/325033477_Equalitar...

[2] https://economics.yale.edu/sites/default/files/marley_finley...

[3] https://fryer.scholars.harvard.edu/publications/empirical-an...