More Gender Equality in Less Religious Societies: Study
Or, people are less religious with education and weakened social strictures. Gender equity is associated with a “modern”viewpoint that correlates with education, etc.
Or... Genders are more equal in countries with less religion
That may well have cause and effect swapped.
I think the role of religion in promoting certain social pathologies is pretty well established now.
I don't know, when many major religions directly call for women to be inferior it seems kind of weird to say it's not causation.
What exactly is the argument? That more religion results in greater distinction between the acceptable roles of men and women? That's plausible enough. But if the implication is that men opt out of religious participation if it does offer increased subjugation of women -- that is a stretch for me.
The real question is does religion do more harm than good?
That is what many in America are asking themselves. And, speaking as a conservative Christian (both theologically and politically conservative, though no doubt the two almost always go together) that represents a sad state of affairs. So if people generally answer your "real question" in the affirmative, what comes next, logically and sequentially in time? They then ask themselves what I will call my "real real question", which is: Do we, do I, still believe in the free exercise of religion as touted in the Bill of Rights? And I think many must be answering that question in the negative if they support helping out parents with private school tuition, but not if their children attend private religious schools. Or if they think it right that a Christian baker should be forced to participate in the celebration of a gay marriage, rather than just refer the couple to an equally excellent baker who has no moral/religious objections to doing the job.