"Rightists"? I'm a liberal, and part of the reason why I go after the woke and their attacks on "problematic" figures is because liberals have had a long history of fighting for freedom of speech, not just as a legal right but as a cultural value. Not only the freedom to speak, but the ability to tolerate speech we don't like.
What Woke Folk are doing now is not only illiberal, it's radically anti-liberal. It's not progressive, it's regressive. Calling for someone to be fired because something they said happened to be considered offensive at that time (Woke Folk are constantly shifting the goal posts when it comes to what's offensive and what isn't) does nothing to foster a tolerant culture.