I wouldn't describe the wokesters as only far left. I think what we've seen develop over the last decade is a second axis that runs from authoritarian through to libertarian - a dual-axis chart.
So it's possible to be:
left authoritarian - the cancel culture we currently see within universities, Big Tech etc
left libertarian - those who tend towards William Morris style socialism, promoting human rights, caring for those less fortunate, small is beautiful, freedom of speech (very important) and so on - John Lennon's "Imagine"
right libertarian - emphasis on individual liberties and responsibility, small government, free enterprise, freedom of speech, the right to bear arms (in the US at any rate)
right authoritarian - The State knows best, our loyalty is to the State, dissent weakens the State, outsiders weaken the state.
The old political parties - from left to right - have yet to realign within a twin-axis political system. Consequently, within any one party, you can find a mix of authoritarians and libertarians - but this is causing a strain on the system - a collapse will come at some point and a new political structure will emerge.