It isn't racist, or even wrong. But one thing that I think is not made clear is that their conception of privilege does not mean any sort of overall advantage. Without that clarity, it sounds like they are making massive, unfounded generalizations about groups of people based on nothing more than their race, which is just a single factor of a person's life. They may be well intentioned, but I don't think their message is clear.
The only solution, ultimately, is treating people like individuals, and acknowledging that within any group that there are massive differences between it's members. Overall trends may exist, and gereralizations can be made, but there's a limit to how much you can assume about an individual based on their membership of a racial group. Any campaign that seems to assert otherwise is problematic.
This campaign might be seen to do that. I don't think that was their intent, but that's what people heard.