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Huh, sure, if the likelihood is a reversed Heaviside step. If the likelihood is itself a Gaussian, then the posterior is a Gaussian whose mean is the weighed average of that of the prior and that of the likelihood, weighed by the inverse squared standard deviations. So even if the st.dev. of the likelihood was half that of the prior for each race, the difference in posterior means would shrink by five times.
Right- there's lots of information out there that will narrow your IQ estimate of someone else more than their race will, like that they're a professional physicist or member of MENSA, but evidence only becomes worthless when it's independent of the quantity you're interested in given the other things you know.