Benefitting from structural privileges is very different from being a racist though.
I think the same principle applies here. Malicious racism and passive racism have the same effect.
For instance, Buddhism is a suite of beliefs about enlightenment and transcendence. We don't refer to people as "structural Buddhists" simply because they have equanimity.
Studies have shown that people who don't think themselves to be actually racist still act in race-discriminatory ways. For example, people with non-ethic-names get more callbacks for their resume controlled for qualifications on the resume (https://www.nber.org/digest/sep03/employers-replies-racial-n...).