This seems wrong.
1. PSpot the fallacy? Well, I don't see any situation where the second premise would ever hold simultaneously with the first. If the second premise is ever true, it must be true for certain instances of ~P. I say certain instances, because, otherwise, we are in the difficult position of positing a moral crime whenever any falsehood is believed to be true. I think that the very act of believing a falsehood can be immoral, but only where there are sufficient grounds for believing the relevant truth (when the truth is known or ought to be known but for the believer's willful ignorance).
2. I am morally barred from believing that P
3. If I am aware of P, psychologically, I must (believe P or believe not P)
4. I believe not P (from 2-3)
5. Moore's paradox(from (1) and (4))
We're left with situations where P is true, but we can't believe it. What possible grounds could there be for believing a falsehood? Well...
(2) is a bit trickier, and may be where the weak point here is. Are there some facts that are so immoral that one should not believe in them even with evidence?This is weak. The "racism is evil" premise implicit in this example only works for a culture such as ours, where the premise is taken for granted. The premise is taken for granted not on instrumental grounds ("Let's all act as if racism is evil, because otherwise nasty things will happen.") but because we believe that racism expresses falsehoods. If "members of race x" really did exhibit moral failings by virtue of their race, then racism would not be universally evil. If we're rocking against racism because the truth is too painful to accept, then we're morally depraved self-deceivers. If, as I think (hope?) is true, racism is despised because it entails belief in falsehoods (or it entails using biased heuristics), then the paradox is not a paradox.
There are some beliefs X such that if you believe them you are evil. Consider a sentence of the form:
#=Members of race x are all liars in virtue of their being members of race x.
Presumably believing # makes one a racist. Racism, let's say, is evil. So believing # makes you evil. One is morally barred from doing things that make one evil. So one is morally barred from believing #.
The paradox arises from treating beliefs like "members of race x have deficient trait y" as uniquely unworthy of consideration. But of course, such beliefs are unworthy because they are members of a certain class of false beliefs - false beliefs where the believer ought to know better. It is because of the constitution of facts in the world, and the relation of the belief to those facts, that racist and other beliefs are wrong.
Now, if we change the supposedly reprehensible premise to "members of race x are all lactose-intolerant in virtue of their being members of race x," the objections surely disappear. Indeed, there must be some distinguishing feature of race x if it is to designate a group at all, so simply by speaking about race x, we are holding as true that members of that race have some quality in virtue of being a member of that race.
Thus, holding a belief about a race must be different from holding a racist belief about a race. If the racist belief is that all members of a certain race are liars, what can that mean? If they cannot help lying, then no moral opprobrium ought to attach to what they cannot help but do; moral condemnation does not accompany the belief. If they can avoid lying but choose to lie at every chance (a remarkable coincidence, to be sure), then I suppose we have a racist belief; but, because each instance of lying is the product of individual choice, what we condemn is not the race but each individual member of the race.
Racism seems, then, to be unjust moral condemnation of individuals in virtue of their being members of a certain race. This condemnation can be unjust if, say, we condemn a person for having a certain genetic characteristic - because the physical composition of the body cannot constitute a moral crime. It is also unjust if we condemn an individual for the actions of others - as when we condemn each member of race x for the lies of all members of the race. In either case, what makes racism evil is moral condemnation; a mere expression of scientific facts about group characteristics could not be racist.
Now, a false belief about group characteristics ought not to be condemned as "racist" simply because it is false. To misjudge genetic patterns is not morally wrong. To assert that, because of those genetic patterns, all members of a certain race are depraved - that is wrong. But then, it is wrong whether or not the scientific belief is true. The truth of a claim about physics cannot justify making it into an ethical claim.
Ultimately, this "paradox" doesn't work because no true belief about the members of a race can be the basis of unfair moral condemnation.