Given the fact that the REPUBLICAN president of the united states talks about going to "war" with American cities, pardoned the January 6 terrorists, posted a video of himself "symbolically" beating up members of the media, and mocked an attack against the family of a democratic member of congress, and he STILL has overwhelming support within the republican party, I find it hard to believe that it is the Liberals who are most cool with political violence.
The majority of the negative rhetoric and "dehumanization" comes from the right wing. They use terms like "libtards" and "snowflakes". And unlike the political left (where such rhetoric seems to be centered on your average citizen/voter), in the case of the republicans such rhetoric goes through the entire core of the republican party, from the garden variety MAGAchud living in his mother's basement posting fan fiction about Trump, right to the party leaders.
Claiming that it is "both sides" that are "fanning the flames of civil unrest" is like saying both Charles Manson and your local jay walker were both "engaged in illegal behavior". While technically true, one side clearly has a greater amount of culpability.
Heck, just look at this shooting... a right-wing celebrity gets killed, and the MAGAchud initially go nuts, talking about a war with Liberals. When the truth comes out that the shooter may not have been the "left wing extremist" that they initially imagined him to be, significant numbers of Trump supporters are STILL trying to push their agenda... "he got radicalized at university" (despite the fact that he dropped out after a semester, from a university that was not known for being a hotbed of left wing thought), "his family said he was left wing" (despite no direct evidence what his exact politics were), etc.