Non-Overlapping Magisteria

When attempting to reconcile religion and science, some people claim that they don't conflict. That's Stephen Jay Gould's idea of Non-Overlapping Magisteria (NOMA). The claim is that science is concerned with how the universe works, and religion is concerned with meaning and morals, and that they are completely separate.

I disagree with this. First, why does religion get to decide meaning and morals? That seems to be philosophy to me. Of course, religion can make such judgments, but gods and the supernatural are in no way necessary for it. I'd just call it religious philosophy.

Further, I'd agree that meaning and morals aren't in science's purview. It deals only with objective truths. But, what good is meaning when it's not based on what's true? Meaning that's based on something that's not true is, well, meaningless.

And then there's always the fact that religion rarely refrains from making scientific claims. Whether or not god exists is an objective truth, and something that science should be able to study.