People on the right participate in cancel culture all the time. It is truly deafening to hear them complain about things they do from their pulpits at FOX, Congress, and Senate.
Anyone who watched TV in the late 90s and early 2000s should be very familiar with how right-wing[0] cancel culture works thanks to organizations like the AFA.
[0] Religious-right, anyway
It wasn't such a partisan thing in the 90s. Democrats let their right-leaning members get away with it all the time. Remember Tipper Gore?