On the left, because they perceive these stereotype validating social studies as supporting racists, deny that stereotypes have any truth in them often against overwhelming evidence.
One side is not more rational than the other. For both, truth has become a casualty to goals. This is a very bad place to be in for the following reasons:
1) If instead of truth standing on its own, you are willing to suppress it to support an agenda (even if it is good), you remove your ability to morally object when someone with a different agenda suppresses a truth you would rather not see suppressed. You are in essence guilty of doing the same thing as the church did to Galileo.
2) It is ultimately counterproductive to your goal. Your suppression of the truth will be used against you by your opponents to good effect. People hate being treated like children with facts suppressed to support an agenda. Once, people realize what is going on, they have a natural urge to support the opposite of the agenda. Think about how atheists use the history of the church suppressing Galileo to persuade people of the danger of religion.
So, if the evidence supports that many stereotypes are generally true, let us accept that what the evidence says. However, that does not mean that we are automatically racists, sexists, etc. As the article says "In situations where one has abundant, vividly clear information about an individual, the stereotype becomes completely irrelevant". By getting to know people as individuals and not just as exemplars of a group can we truly overcome injustice. In addition, by acknowledging the truth in stereotypes we can then work to remedy underlying causes for some of the negative stereotypes.