The "cost" should not matter. We are either fair to people we have wronged, or we are not, and we look for excuses, such as worrying about the "cost" or determining who else has suffered "injustice." NO group, with the exception of indigenous Americans, has suffered more than the descendants of slaves.

"Woke" is not a term originating with Black Lives Matter. Black Americans have used the term for decades, at least. It is a warning to be alert to the presence of racists.

Perhaps you should be braver about what you think and less worried about what others will think you represent something other than "neutrality."