The fundamental quality of someone being “anti woke” is a claim that they won’t accept being told how to behave.
Except that we’re told how to behave all the time. Traffic laws, mortgage payments, workplace responsibilities — living in civilized society is about agreeing to compromise one’s independence. Freedom is not absolute.
Being anti woke is about refusing to be told what to do on specific subjects by specific kinds of people. It is, inherently, a statement that “those people” do not have the authority to impose such a demand. It is fundamentally an assertion of status. “You people don’t get to tell me what I can and can’t do.”
In short, then, being anti woke is absolutely a form of bigotry, but it’s the kind of quiet, insidious, indirect bigotry that gets a pass when our media narratives condition us to expect racism etc. to look like the Klan and other overtly violent and hostile forms of direct oppression.