It's possible for there to be no problem with white people, regardless of how "white" they are being, while there is still a big problem with structural barrier

It's possible for there to be no problem with white people, regardless of how "white" they are being, while there is still a big problem with structural barriers to others moving to areas that might otherwise be the best choice for themselves and their family. I think the parent intended the latter, pointing at overwhelming prevalence of white people (rather than - as you seem to have read it - overwhelming... intensity(?) of white people) as being an indicator of the persistence of such barriers.