Woke branding works by connecting on a personal level with the customer and generating trust. Don't let it be a facade that will crumble with time; become what you want to be perceived as.
The people your work with and the people in your team will impact the message you want to communicate directly and support your intentions. Nothing shows more commitment than being surrounded by equally committed individuals.
If you can build a brand around a cause, make sure it's one you and your team believe in and genuinely embed it into your brand through the people you hire, the product you sell, and the management style you choose. Your brand should leave and breathe this idea.