For what it is worth, to me, the phrase “cancel culture” does not mean cancel or forget history. Similarly, it does not mean forget about cultures or cultural differences.
Instead, the term “cancel culture” is best thought of (by me) in terms of eradicating a cheap political weapon, “culture wars.” The latter term is all too conveniently summoned by those (in media and politics and elsewhere) who view history, culture, time and space as stagnant, never changing, caught in a space and time warp. That way, everyone can be faux “surprised” and “shocked” and have something to chit chat or argue about.
I think the term “cancel culture” is an attempt to end the “culture wars” used by those in power or powerful positions, to divide, oppress or alienate anyone, or any group, even for a short time in history.
The term “cancel culture” is not meant to infer cancel history, however beautiful, ugly, sensitive and caring or cruel that history may be; instead, “cancel culture” is intended to mean cancel weaponized culture.
Weaponized culture, used against whole or partial segments of any population, should be relegated to the trash bins of history, quickly.
Nonetheless, we should never forget history, even if toxic or culturally weaponized for a time.