This is a very strange failure of reading comprehension. I think you're trying to write "I will only give you food if you're white." Are you trying to say this sentence is incoherent? I admit that if you say this sentence to a black person, it is logically equivalent to "I will give you food if you change your immutable characteristics". But they are not logically equivalent in general, so your gotcha doesn't apply to my argument.
About your actual argument: a) it is obvious they don't have constitutional protections, I am not arguing about the law, this is an ethical point; b) identity-group prejudice is not the only kind of unethical behaviour. Since you mention prejudice, I think you proved my point - if the ethical standard was "nobody is materially worse off" then this kind of prejudice would just be irrelevant. If the US had a "whites only" immigration policy that would be A-OK with you, they have no obligation to let people in. If that's your ethical standard, I have nothing more to say.