I think you’re mixing up situations. Child abuse doesn’t mean white privilege doesn’t exist
Refusing to investigate crimes because you don’t want to be accused of racism does mean white privilege doesn’t exist. If you are a 14 year old white girl who has no access to the justice system because your abuser is from a more favoured race, then you do not have white privilege.
If those girls had ‘white privilege’ when they reported abuse by non-white men, the justice system would instantly swing in to action. It didn’t. Over 40 years. Across the country.
In fact, the situation has been akin to those found in the Deep South in the worst abuses of the segregationist era. The services refused to act despite appalling crimes because they privileged one race over another. In the Deep South white people could do appalling things to black people confident in the knowledge they could do it because the authorities wouldn’t get involved. Exactly the the same thing has happened in Telford and Rochdale and Rotherham.
So yes, it does mean white privilege doesn’t exist when the police won’t investigate crimes on the basis that you are white and your attacker is not.
One of the biggest criticisms of intersectionality is that it treats wealth inequality as just another characteristic which leads to oppression, rather than recognising it as a mechanism of oppression in itself..
Besides, Intersectionality has been used to justify some singularly unpleasant behaviour and ways of thinking. Particularly those which are most damaging to the white working classes by creating inverse hierachies, particularly those which justify black people saying and doing absolutely appalling things on the basis that they ‘can’t be racist, because they don’t control the power structures in society’.
I think a 12 year old girl who can’t get the police to prosecute her rapist might have a few choice things to say to anybody who suggested that she benefited from societies power structures.