What some on the left is doing is reprehensible, however, holding people to account for their words is not an outrage, so there's nuance there that can only be discussed with respect to specific cases. So, if you have a specific example of cancel culture that you think is an egregious example of it on the left, by all means bring it up. I suspect that many (not all) cases of so-called cancel culture on the left are being amplified by the GOP because it suits them to deflect from what they're doing.
Several of the Republican representatives that voted for Trump's impeachment were censured by their home state Republican parties. Whilst censure is relatively toothless, it's probable that it will affect their chances for re-selection when that comes up. Some moderate Republicans in state legislatures and other bodies have resigned because of the slavish adherence to (and bullying on behalf of) Trump by other, more established individuals in those legislatures and bodies. Cancel culture is alive and well in the Republican party, and has been for decades.
I presume that you're just quoting selectively, but if your associates aren't also horrified by what the GOP are doing then I have to wonder if they're paying attention. The GOP just tacitly supported a coup, a regular feature of authoritarian regimes; they support gerrymandering, which is a version of another tactic of authoritarian regimes (run elections that are exercises in futility); and they accuse the opposition of doing what it is that they're doing (because shifting blame onto the opposition is also what authoritarians do).
I have a lot of concerns about what the Dems are doing, but they aren't sowing division at every turn and deepening the partisan divide. If they were, they wouldn't have (already) capitulated on so many election promises that were anathema to the GOP.