Funny, I too feel that free speech is under threat, but not from the 'woke' but the new, vocal, intolerant conservatism (which isn't even really conservatism as we know it) and their supporters who actively vilify any opposition (the Jeremy Corbyn and Rebecca Long Bailey smear campaigns) or try to silence groups of people who campaign for equal rights such as BLM or environmental activists (see Police, Crime, Sentencing and Courts Bill), or try to restrict underprivileged groups' right to vote (photo ID being made compulsory to vote).
My values have always been aligned with the left but I didn't really engage in/follow politics until the Brexit vote which was the first jolt for me to this new reality, and then the 2019 general election and the Conservatives' brazen lies during their election campaign and their subsequent failures and messes, none of which appear to hurt them one bit, if anything the opposite. Since then a gradual chipping away at civil liberties, undermining the national, impartial broadcaster, and so on.
I was always friends with people who I knew were on the right on politics, socially etc, but didn't really speak up about my opinions, because I suppose I didn't feel my right to exist peacefully in this country (EU national) and express opinions as I saw fit was under threat! Silly me.
I'm not allowed to vote in general elections but expressed my support for the Labour party on social media leading up to the 2019 general election, and have posted quite a bit in support of BLM, about violence against women and girls, LGBT rights etc. I've been taken aback by the number of people who have since unfriended me or blocked me on social media or even complained about me in a professional setting when I expressed pro choice views on a social media chat. The same people who refer to millennials as 'snowflakes' and who wage war on the 'woke brigade' for apparently stifling free speech.
I have witnessed the discomfort and irritation of men when you bring up women's right to equal treatment (not being catcalled or harassed on the street, not being ridiculed or undermined in the workplace, not being subjected to everyday sexism), respect, equal pay and bodily autonomy (rape culture, reproductive rights). You get labelled as a troublemaker and a pain in the arse while the men remain the good guys.
It's not 'the woke' who are the threat to free speech.