The formula of humanity itself makes clear when it is stated that it is precisely not intended to distinguish between persons:
"So act that you use humanity, whether in your own person or in the person of any other, always at the same time as an end, never merely as a means" (Ak. 4: 429).
The point here is that humanity, whether it is found in oneself or in any one else should always be treated as an end, due to its status as an end-in-itself. Since this is so the specific possession of it in a given individual cannot be the point. This is the source of an argument against Kant since the partiality that is at work in personal relationships may seem thus ruled out. I don't think that this is so but don't want to argue this question in this particular posting. Instead, I simply want to point to the formulation as ruling out the understanding that what is specifically of interest to Kant in the formula of humanity can be some special status ascribed to individuals. The point of the formula of humanity seems to be precisely to argue against such a view.
Implications drawn out from the formula of humanity concern the nature of law. So Kant later argues that we are subject only to laws given by ourselves which are nonetheless universal. When formulating this point Kant also makes clear the ground of the respect attaching to humanity stating that it is the possible giving of universal law that is the proper object of respect and that "the dignity of humanity consists just in this capacity to give universal law, though with the condition of also itself being subject to this very lawgiving" (Ak. 4: 440).
This claim is the basis of Kant's cleavage between moral theories grounded on autonomy and those that are in their basis heteronomous. Only the former give the true inner ground of morality according to him so any theory that based morality on something else would fall into the area of the dialectic of morality. If there are grounds then for partiality, and I will suggest in a later posting that there are, such grounds are not formulated and could not be formulated by taking individuality as a prime moral value where this value was taken from the formula of humanity. So Nozick's attempt to suggest otherwise is not faithful to Kant.