I've noticed an unthinking strain of anti-wokeness along with the thoughtful criticisms, but I haven't come across anti-anti-wokeness.

Do you have an example that illustrates how anti-anti-wokeness differs from wokeness? One of the core problems with wokeness is its extreme difficulty in recognizing any problems with its ideas. Why isn't anti-woke rejection of woke ideas treated just the same thing as conservative or liberal or other rejection of woke ideas?