I don’t know.
To be more precise, it seems obvious to me that religion causes both harm and good. What I don’t know is whether the harmful effects happen more often than the beneficial ones (or if the former somehow qualitatively outweigh the latter). Allow me to explain.
It seems to incredibly simplistic to say either “religion is always bad” or “religion is always good.” There are clearly people who are motivated, by religion, to do good things, such as donate their money to charity, do volunteer work, be honest, kind, compassionate, etc. The fact that such people exist disproves the claim that religion is always bad. (Nontheists may think that such theists are doing the right things for the wrong reasons, but that is irrelevant. Such people show that religion can be good.)
Of course, there are also people who are motivated, by religion, to do bad/evil things, such as fly airplanes into buildings, execute others who renounce their religion, oppose scientific progress, protest at funerals, etc. The fact that such people exist disproves the claim that religion is always good. (Theists may think such people are doing the wrong things for the wrong reasons, but that is irrelevant. Such people show that religion can be bad.)This is why I think a better approach is to admit that both outcomes are possible and instead try to figure out what is more likely.
I’ve yet to find anything in writing which actually tackles this issue in an intelligent way. In my experience, what usually happens is some atheist will point to examples of bad things done in the name of religion; the theist will respond by saying the actions are inconsistent with the ethical teachings of the religion and/or point out atheist atrocities. What nobody seems to do is to analyze this in a statistically valid way, by figuring out what is representative of theistic behavior and secular behavior. That’s much harder than tossing out “what about the crusades?” and “Stalin killed millions of people!” epithets.
The fact that a claim is hard to justify doesn’t excuse making the claim without justification. The moral of the story is that people should stop making claims about whether atheism or theism lead to an overall balance of good (or evil) unless they can back up those claims.
As an epilogue, if anyone is aware of a study which does try to do this, I’d love to hear from you.