Interesting analysis. I agree that the left have become 'Blairite', i.e. more representative of "big banks, corporations, professions (always teachers, but now also lawyers and doctors)", and that the right has become populist, if by that you mean 'Trumpite'.
However that has little to do with 'cancel culture' which I believe is one of the many culture wars and therefore largely non-political. I'm mostly against it - fatuous and offensive positions should be exposed to view so they can be mocked, rather than cancelled. But I still am no wiser as to what 'woke' actually means.