>is tantamount to saying that they're a bad person and they should feel bad
What makes you (hypothetically) a bad person is having privilege and supporting policy which benefits the privileged at the expense of the unprivileged. The blame is assigned not for being a member of a privileged class, but for forming and acting on political opinions (including acceptance of the status quo) based on that privilege.
People who use privilege as an argument aren't asking you to be ashamed of being white, they're asking you to be ashamed of being conservative.
What makes you (hypothetically) a bad person is having privilege and supporting policy which benefits the privileged at the expense of the unprivileged. The blame is assigned not for being a member of a privileged class, but for forming and acting on political opinions (including acceptance of the status quo) based on that privilege.
People who use privilege as an argument aren't asking you to be ashamed of being white, they're asking you to be ashamed of being conservative.