I don't agree completely that IQ cannot be measured.  The question is like everything else in science: how accurately and precisely and what are you measuring.  

Intelligence research like all the other "social" science is a very inexact science.  In has however to some extent been reconnected to actual evidence by advances in genetics.  It is now crudely able to predict someone's IQ based on DNA.  The important point is IQ was never intended to measure intelligence.  It's intended purpose was to help people make career or life choices.  It was discovered however that general intelligence could be approximated from IQ scores.  How accurately and precisely cannot be answered.  The reason that I bring this up is that it should be a matter of common sense that there is a genetic component to intelligence like anything else.  Likewise common sense tells us that culture or nurturing plays a role.  It turns out that intelligence is a necessary but insufficient condition for success in almost every aspect of life.  How IQ fits into this equation is evident in the difference between the rates of divorce according to IQ.

Before IQ became an important determinant in economic success due to advances in technology and social complexity divorce was more uniformly distributed.  The Matthew principle tells us that success in one area will lead to success in other areas.  The more resources you have, including intelligence, the better chance you have of coping with challenges.  There is a compounding effect that has resulted in increasing economic and social disparity.  IQ it turns out is doing exactly what it was intended to do, determine the probability of success.  

What role then does culture play in IQ?  You may have heard of the Flynn effect.  What you probably have not heard is that it is an illusion.  Most of the gains in IQ can be attributed to better nutrition and other environmental changes.  But the Flynn effect has slowed or even reversed in recent years.  What culture is now providing is the ability to do well on tests.  The real evidence suggests that general intelligence may actually be declining.  Biology has become the enemy probably because of the mutation rate in populations not subjected to harsh selection.  We don't like it but nature is cruel.

The other thing that is missing in the above discussion is the nature of culture and its relationship to "intelligence".  To understand culture you have to go back to the beginning.  Humans don't have tools because they have larger brains they have large brains because their ancestors started using tools. People have turned this biological equation on its head because the implications are unpleasant.  They hold the contradictory opinion that intelligence is an innate property but at the same time want to argue that it can be altered by changes in culture.  The confusion in part arises because changes in the environment do affect intelligence.  What they are missing is that culture itself is part of "intelligence".  Our intelligence is artificial in the sense that nobody is born smart. No society is born "smart".  There is a long evolution of cognitive tools we call culture that have made people ``smart".  It's a kind of swarm intelligence that is passed down from generation to generation.  Do what you like to the biology but without swarm intelligence people are as stupid as apes.

How does any of this alter the discussion?  Not much other than that culture bigotry is not what people think it is.  Mostly because like other aspects of biology group selection has implications they find unpleasant.  Most of the difference in human intelligence seems to be a matter of group selection, including the cultural contribution.  Not only are the ramifications of natural selection unpleasant but so are those of cultural selection.

What does any of this have to do with race?  Not much is the answer.  Race is an abstraction.  It's a very inexact classification system based on superficial characteristics.  There is more genetic variability in Africa than anywhere else in the world because of the nature of evolution.  Africa, it turns out based on DNA, is full of "races".  So many in fact that it would be impossible to sort them out with any reliability.  The same principle would apply to a lesser degree to the rest of the world.  The question becomes why would you want to do that.  If the answer is innate predispositions to group select you see the problem.  The problem isn't group selection itself.  It isn't even bigotry.  The problem is in how it limits cultural evolution.  In how it limits solutions that benefit the most people.  It's why when talking about IQ we don't include race as part of the equation.  What we want to talk about is how to integrate social economic classes in a way that they can take the most advantage of cultural intelligence.                 

Correction Fourth paragraph..."The real bigotry is the desire (for) there to be inferior races...."

Good post! Agree 100%.