Both the woke left and the reactionary right want to shut their opponents up. In the case of the wokes, the instrument of choice is a mob on the internet; the right, on the other hand, uses the government to do its dirty work. Both groups claim to support free speech, but only liberals really do.
Over the last two years, the right has been winning on this issue. First, it succeeded in shutting down discussions of race and gender in schools in red states; more recently, it has weaponized antisemitism for two purposes: to create a wedge between liberal and progressive voters before the election; and to brand the views of the latter as morally illegitimate.
There are lessons in this for both woke progressives and liberals. For liberals, it is essential to protect the right of progressives to speak, even when, as in the case of Gaza, they may not agree with progressive opinions; the decision of the administration of Columbia University to fold in front of GOP hardliners and crack down on pro-Palestinian demonstrators was a terrible mistake. Progressives, for their part, need to understand that the culture wars are a war on them, not the moderate left, and that only the liberals they so enjoy abusing stand between them and enforced silence.