It's true that those who are truly woke have a viewpoint that could be characterized as "white supremacy"; they believe that:

• Western civilization is inherently white civilization
• Western civilization is inherently dominant
• Race, and its intersection with other identities, should be the central focus of political discourse
• Meritocratic systems lead to white people being at the top
• Non-whites are inherently ill-suited to Western civilization, so to accommodate them it must be radically changed

(Note that this is a more extreme position than most people characterized as "white supremacists", who would be likely to disagree with the second and fourth statements above).

Their other beliefs are not exactly "white supremacy"; they believe:

• The dominance and superiority of whites is a bad thing [Tim's point above]
• Race is purely a socially-constructed phenomenon with no biological basis
• All morality is culturally relative, except for "oppression", making whites inherently morally inferior
• The only reason for whites' superiority is this "oppression" - essentially "superiority" is equated with evil
• They themselves define "white supremacy" as not supporting the tearing down of Western civilization - by their own rules, they aren't "white supremacists"