You are confusing correlation with cause. The same factors that cause people to maintain a strong belief in religion -- poverty, lack of education, lack of communications, remote settlements -- also cause high infant mortality. The solution is to fix the causes -- which is happening, fortunately, though more slowly in some places than others.
I sort of agree, and sort of disagree. One: the opinion is not mine, I merely published it here for discussion. Two, the correlation is strong, but as you observe, correlation is not always causation.... I would argue that there is a strong component of causation by religion, even if it's not the sole cause - however, it's inarguable that religion causes lack of education and keeps people in poverty. So, my overall take is that religion is one of several direct causes, as well as a second-order cause or enabler of some of the others.
Even if religion isn't a causative factor itself, the point is that it doesn't help anything. If religious faith helped people to take care of important factors in life, such as the health and well-being of their nation's children, then it would be a valuable and important belief for people to have and they would benefit from holding that belief, regardless of how accurate the belief may be.
Not only is religious belief fictional, however, it's also not a helpful thing which makes a positive contribution to one's society.
Again, this is not necessarily the case. As much as I hate to argue in favour of religion, the fact is that it brings large amounts of funds --and some skilled workers -- from the developed world into the Third World, and generally seeks to use them where they will do the most good. It's quite possible to argue that if religions didn't do this then governments and secular groups would be forced or shamed into doing a better job of it themselves, but the fact is that they do.
The one thing that lifts people out of both religion and high infant mortality -- as well as other indicators of misery -- is affluence, and the most direct route to affluence is via democracy, free trade, respect for personal property and the rule of law. But these things take time to establish and gain acceptance, and in the meantime anything that gets welfare to people who desperately need it deserves our support, however much we disagree with the motivations behind it.
You are assuming the correlation is causation. There is another possibility. The conditions that cause infant mortality (poverty , lack of education) are also the conditions that allow religion to flourish, because it give 'hope'. Mind you, education and jobs would help better, but religion is probably not the cause, but an effect of the conditions.