Aside from the fact that the highlight findings from the Politico cancel culture poll are tainted by question wording and priming effects, I'm not sure they actually tell us much. The key numbers IMO are all the way at the bottom of the piece, in this para:
It's not surprising to me at all that people think cancel culture is bad when a pollster describes it as group shaming and infringing on free speech before they ask the Qs. That most people think social consequences for offensive speech are justified is the real headline here.
Anyway, people who are on Twitter too much talking about cancel culture are probably going to share the headline numbers far and wide, but once you actually dig into the story it's clear that the public is having a much more interesting and substantive debate.
(A debate that shows the public actually sympathizes with the "cancellers" a lot more than the poll or the article lead us to believe.)