I would encourage you to reflect on what you think "woke" is, and why things that you think are woke are mutually exclusive from the skills and qualities you value.

"Woke" is a nonsense scare phrase at this point, when what you're actually taking issue with is valuing people's lived experiences and backgrounds as a part of what they contribute. Understanding where people come from and how that colors their world view is simply a good practice when doing anything, but especially when you're trying to do science/academia. Too many similar minds in a room will never produce what one with a diverse group will. Diversity is good science, and valuing it is not "woke".