Now I'd probably be called a bit of a Lefty by some on here, and I've been called a bit of a Tory by Corbyn supporters in the past, which is how I like it - if you're fully in a 'camp' you're probably not thinking for yourself in my opinion.
Now I know people that have the sort of opinions that are defined as 'woke', I share many of them myself, but these folks are not intolerant and are happy to engage in lively, indeed often humorously insulting, conversations about their opinions. To me that is how we all get to revise and develop our ideas.
The problem is intolerance for other's opinions and condemning anyone who disagrees. This isn't a left or right issue but an authoritarian/intolerant v libertarian/anarchistic/tolerant one. In the US and UK, currently the left seems to have more people like this. In other parts of the world, it's the right.
I'm the 'while I may disagree with what you say, I fully support your right to say it' sort.
DS