For me, science is just one way of examining and knowing the world. Only phenomena that is regular, repeatable, and reducible to simple laws falls under the purview of science. Let’s not even talk about theology - there are many areas of human experience which natural science cannot model accurately, much less predict. Some atheists would retort, “But in principle everything, including human history, consciousness, ethics, and religion, is reducible to physics!” But this is more of an article of faith and expression of optimism in future science than anything with direct empirical proof.
Now when we put God into the picture, the limitations of science become even more apparent. God, if he exists like the Judeo-Christian conception, would be the Creator, Sustainer, Sovereign of the universe. When one claims that one can “scientifically” rule out the existence of God, one is really claiming that science should be able to fully model God’s actions in the universe. But why should this be the case? If God exists, he is the one who is responsible for the order and regularity that makes science possible in the first place. This would be like ants trying to decipher the actions and motivations of myrmecologists.
These reasons are why I think science is extremely limited as a tool for assessing the existence and actions of God in the universe. It’s only able to rule out some scenarios. For example, science cannot rule out miracles for this purpose. By definition, miracles are special, unrepeatable events with special significance. Through scientific lens, miracles are “five-sigma events” - events which if they happen, a scientist would likely interpret as a malfunction in equipment causing anomalous data points. A good scientist would reset their equipment and try to see if the anomaly happened again. If it didn’t, then the data point would be tossed out. This illustrates how unequipped science is to handle miracles.
A common error is to think that “once X has been explained through the lens of social psychology/cognitive science/biology/physics/etc. it means it is purely naturalistic and has nothing to do with the supernatural.” But this is falling into the error that God is regarded merely a placeholder for phenomena we haven’t understood yet. Thus, every time some phenomena is explained, God becomes less necessary.
On the contrary, a Christian believes that God is sovereign over all aspects of existence, including social psychology, cognitive science, and physics. Thus, even if aspects of religion can be explained through the methods of psychology, that doesn’t mean that’s all there is to it. God may still exist even if aspects of his actions are intelligible through the lens of science.
This is similar to how I can explain that you, as an educated Western person living in a society which respects science and scientists, is more likely to be convinced by Newtonian mechanics compared to someone living in a hunter-gatherer society. Such an explanation does not reduce Newtonian mechanics into a purely sociological phenomena divorced from reality. We can still believe that Newtonian mechanics is objectively true. A similar logic can be applied to science-motivated explanations of religion.