It doesn't follow that there aren't racial difference based on genetics as well. In fact, the idea that there might NOT be is quite absurd. Of course there are. The only question is how large they are.
That is not the only question. The question that gets people into trouble, is "which groups are favored or disfavored". You can't answer that without offending some people, no matter how small you think the genetic component of the difference is, because many of the people who read it will discard or forget the magnitude entirely and look at only the sign. Saying that group X is genetically smarter than group Y by 10^-10 IQ points will, for many listeners, have the same effect as saying that X is 10^1 IQ points smarter. And while the former belief may be true, the latter belief is false, harmful to those who hold it, and harmful to uninvolved third parties. True statements about race, IQ, and genetics are very easy to simplify or round off to false, harmful and disreputable ones.
That's why comments about race, IQ, and genetics always have to be one level separated from reality, talking about groups X and Y and people with orange eyes rather than real traits and ethnicities. And if they aren't well-separated from reality, they have to be anonymous, to protect the author from the reputational effects of things others incorrectly believe they've said.
(Edited to add: See also this comment I previously wrote on the same topic, which describes a mechanism by which true beliefs about demographic differences in intelligence (not necessarily genetic ones) produce false beliefs about individual intelligence.)
The important thing for me is that the standard deviations swamp the average difference, so the argument against individual prejudice is valid.
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