one thing the left seems to talk about a lot, but not really understand, is personal bias. The left talks about racial bias, sexist bias, and so on, all of which are subconscious, and this is known to be a scientific fact. However, one thing I often see left-leaning individuals fail to recognise is their own bias towards language. The left is very stifled in terms of language, due to concerns about offending people or making social mis-steps around people of specific assigned minority groups. And yet, the left is often willing to direct these deemed-offensive patterns of communication against groups deemed "fair game", such as males or whites. Hence you will often find left-leaning commentary similar to "white people need to X" or "white men are ruining Y". You would never see these phrases directed against black or gay people. My point is that the mainstream left believes in (or at least tolerates) an asymmetric treatment of people based on unchangeable characteristics. The rationale is around how this is "punching up" or that power imbalance between groups makes race-based attacks acceptable or unacceptable in different circumstances, but the key thing you need to understand is that the right is vehemently opposed to this concept and in many ways takes the complete opposite approach.

Modern conservative communication (I'm talking about younger conservative movements - The_Donald, Breitbart, you name it) doesn't generally care what race or gender or orientation you are, and will attack or praise you based on your ideas alone. When right-leaning outlets or communities make anti-muslim comments, the left-wing assumption is "my conception of a muslim person is brown, attacking a brown person is racist, this person is racist" but in actual fact the criticism will often be about perceived cultural incompatibilities. A conservative may criticise BLM or promote "all lives matter", because they oppose racialising police brutality (an issue that is much more closely tied to economic station than race) or some of the acts of BLM-backed groups. In the interpretation of the left, BLM is a civil rights group for black people, the conservative is attacking a black civil rights group, therefore the conservative is racist. The modern right also often goes out of its way to subvert political correctness by using offensive language, for the express purpose of offending the left and in-group signalling to the right. See Milo Yiannopoulos, a gay Jewish man and figurehead of modern conservatism, making Jew jokes at his own expense or talking about how gay he is in thinly-veiled stereotypes or references. And he seems to have fun doing it. Do you really think that a racist or homophobic movement would have people like Milo, Sheriff David Clarke, Ben Shapiro and so on as figureheads if they were motivated by hatred of gays, blacks or Jews?

I hope you don't take this as an attack as it isn't intended as such - but there's a lot of context to understand if you want perspective from the other side of the aisle. I personally see the right as more egalitarian than the left in modern times as it more closely follows MLK's dream of judging people "not by the color of their skin, but by the content of their character".