Renouncing sin is very different from feeling guilty about it. The second might be a step toward the first, or it might just be pissing in bed. The purpose of a profession of guilt is often precisely to avoid doing anything substantial about the issue in question.
I think the way one would get White people to renounce Whiteness would be show them that there was something better than Whiteness. The only way I can think of doing this is to go to the underlying class war, which I think resonates and drives the construction of Whiteness. Some less fundamental remedies are objectively possible, I suppose, but there don't seem to be enough White people interested in them to get anything done; and in any case the energy of the class war will simply produce other social pathologies.