I always read accounts like this letter is addressing, and by all personal reckoning, your (very common) observation is exaggerated, and assuming you are expressing it honestly (and not just as political-team-booing), I think you shouldn't be worried about cancel culture practically affecting your children. The vast majority of the time, somebody being described as a victim of cancel culture was really either A. Strongly criticized or even harassed, which has been a permanent fault of people on all sides of political topics forever, and in fact seems even more severe coming from people of the opposite ideology to cancel culture, or B. Was fired for genuinely hateful/immoral behavior. I.e. the cases where cancel culture actually misfires, usually due to a misunderstanding that catches on (the primary danger of cancel culture), are apparently few, relatively speaking (though of course one's political loyalties tend to color the perception of what counts as unjust consequences).
I think the much more concerning, practical danger to our childrens' intellectual health and spirit is the more general phenomenon of extreme political hatred (see point A. above).