Opinionated in a Linux context means specific design choices, and a setup not for a wide audience but for a specific audience. In this case mostly programmers. That has nothing to do with "woke" or "non-woke".
I have not been aware of it being pushed as "non-woke". Can you add a primary source for that claim? I could not find "non-woke" anywhere on the Omarchy site or its manual.