(Disclaimer: This post is sympathetic to a certain subset of theists. I am not myself a theist, nor have I ever been one. I do not intend to justify all varieties of theism, nor do I intend to justify much in the way of common theistic behavior.)
I'm not adopted. You all believe me, right? How do you think I came by this information, that you're confident in my statement? The obvious and correct answer is that my parents told me so1. Why do I believe them? Well, they would be in a position to know the answer, and they have been generally honest and sincere in their statements to me. A false belief on the subject could be hazardous to me, if I report inaccurate family history to physicians, and I believe that my parents have my safety in mind. I know of the existence of adopted people; the possibility isn't completely absent from my mind - but I believe quite confidently that I am not among those people, because my parents say otherwise.
Now let's consider another example. I have a friend who plans to name her first daughter Wednesday. Wednesday will also not be adopted, but that isn't the part of the example that is important: Wednesday will grow up in Provo, Utah, in a Mormon family in a Mormon community with Mormon friends, classmates, and neighbors, attending an LDS church every week and reading scripture and participating in church activities. It is overwhelmingly likely that she will believe the doctrines of the LDS church, because not only her parents, but virtually everyone she knows will reinforce these beliefs in her. Given the particular nuances of Mormonism as opposed to other forms of Christianity, Wednesday will also be regularly informed that several of these people are in a position to have special knowledge on the subject via direct prayer-derived evidence2 - in much the same way that her parents will have special knowledge of her non-adopted status via direct experience when she wasn't in a state suitable to notice or remember the events. Also, a false belief on the subject could have all kinds of bad consequences - if the Muslims are right, for instance, no doubt Hell awaits Wednesday and her family - so if she also correctly assumes that her parents have her best interests at heart, she'll assume they would do their best to give her accurate information.
Atheism tends to be treated as an open-and-shut case here and in other intellectually sophisticated venues, but is that fair? What about Wednesday? What would have to happen to her to get her to give up those beliefs? Well, for starters, she'd have to dramatically change her opinion of her family. Her parents care enough about honesty that they are already planning not to deceive her about Santa Claus - should she believe that they're liars? They're both college-educated, clever people, who read a lot and think carefully about (some) things - should she believe that they're fools? They've traveled around the world and have friends like me who are, vocally, non-Mormons and even non-Christians - should she believe that her parents have not been exposed to other ideas?
Would giving up her religion help Wednesday win? I don't think her family would outright reject her for it, but it would definitely strain those valued relationships, and some of the aforementioned friends, classmates, and neighbors would certainly react badly. It doesn't seem that it would make her any richer, happier, more successful - especially if she carries on living in Utah3. (I reject out of hand the idea that she should deconvert in the closet and systematically lie to everyone she knows.) It would make her right. And that would be all it would do - if she were lucky.
Is it really essential that, as a community, we exclude or dismiss or reflexively criticize theists who are good at partitioning, who like and are good at rational reasoning in every other sphere - and who just have higher priorities than being right? I have priorities that I'd probably put ahead of being right, too; I'm just not in a position where I really have to choose between "keeping my friends and being right", "feeling at home and being right", "eating this week and being right". That's my luck, not my cleverness, at work.
When Wednesday has been born and has learned to read, it would be nice if there were a place for her here.
1I have other evidence - I have inherited some physical characteristics from my parents and have seen my birth certificate - but the point is that this is something I would take their word for even if I didn't take after them very strongly and had never seen the documentation.
2Mormons believe in direct revelation, and they also believe that priesthood authorities are entitled to receive revelations for those over whom they have said authority (e.g. fathers for their children, husbands for their wives, etc.).
3I have lived in Salt Lake City, and during this time was, as always, openly an atheist. Everyone was tolerant of me, but I do not think it improved my situation in any way.
"...what is some evidence that theists are less [rational] than atheists are?" is an incomplete question.
(tl;dr By talking about theists as a group, we are organizing people around their belief in something false that they generally should not believe in that both causes and is correlated with more general irrationality. Other than the criteria we used to organize the group, we shouldn't expect to find many other universals, just significant patterns with exceptions.)
Are all theists less rational than all atheists are? Obviously not, under any important definition, for the same reason each person who eats 4000 calories and less than 50g protein daily is not less healthy than each person who eats fewer calories and more protein, and each person looking at a Japanese newspaper does not speak better Japanese than each person not looking at a Japanese newspaper speaks Japanese.
We can still say important things about the basis by which we organized people into these groups. They can have both direct causal effects and statistical significance from indirect links to other measurable things. For example, looking at a Japanese newspaper can cause one to get better at speaking Japanese, and looking at a Japanese newspaper is correlated with having Japanese relatives who help one learn Japanese.
Finally: all else equal, looking at a Japanese newspaper is better than nothing for learning Japanese, and it's also better than what most people are doing now for learning Japanese.
If we're organizing people into "theist" group and a second group made of everyone else, "theists are less [rational] than atheists are," represents some different notions that have different proper responses among them.
If the assertion is "being a theist is correlated with being irrational (and/or playing the banjo, etc.)," then that claim needs to defer to science and new evidence, as I think you are saying.
I say "defer to" because there is an appropriate confidence someone with my amount of evidence should have in the claim. I feel very comfortable claiming that the top contributors to lesswrong are almost certainly not also the top contributors to the magazine Seventeen, despite a dearth of scientific studies on the subject.
It may be worthwhile to discuss the amount of confidence someone with a certain amount of evidence should have in a specific claim. My first response to a claim like "People who believe the soul influences some human speech (or theists, or whoever) are, on average, as rational as those who believe speech is not influenced by a soul," or "The (first? I'm not sure what conspiracies are popular) moon landing was faked," is to ask about what evidence the claimant currently possesses and how they process it. This is often more important than determining the truth of the original claim, which often will be best determined by gathering new evidence. In such a case, what's really being discussed is not the truth of the original proposition, but the reasonableness of the original statement, so no evidence on its truth is relevant.
If the assertion is "being a theist causes irrationality," truths are entangled. That's not a dogma I cling to, and each individual has other influences in his or her life that may make them an exception, but I'd like to hear some kind of response to those arguments or I won't feel obliged to go looking for evidence (unless something important hinges on my being right).
This depends on theism being irrational, which I think it is for most people - not having conducted studies, of course. For many people, theism is rational, particularly the very young, who should notice a pattern forming in which their parents are eventually right about things the child does not understand because they are too complex.
This does not depend on acts (such as thoughts) designed to induce a belief in theism being irrational.
If the assertion is "all else equal, a person with a given set of beliefs is more rational without the additional belief of theism," then yes, on average...if we have organized all human minds by their belief in a proposition that most should think false, then those who are inappropriately theist are many, those who are inappropriately atheist are few, those who are appropriately theist are few, those who are appropriately atheist are comparatively many.
If the assertion is "based on the knowledge held by the reader of this sentence, he or she is almost certainly being irrational if he or she is theistic," that is true with a good deal of help from selection bias, but one could say a similar thing about American adults.