UQD, do you accept the point that the scientific procedure of making observations, forming a hypothesis, seeking to confirm or disconfirm it by gathering more observations, refining the hypothesis accordingly, is a procedure for understanding empirical matters, yes?
It is not, for example, how we reach mathematical truth, or logical truth. So there is at least one form of truth-seeking that it non-scientific (not anti-scientific).
And of course there is non-scientific reasoning, philosophical reasoning, that stands behind science -- e.g., most simply, we ask ourselves all the standard sorts of questions about 'what is it for empirical objects to exist, to be known, to be meaningfully spoken of?
Science is one sort of intellectual enterprise, geared to empirical questions. Even accepting that there is only a material world -- nothing supernatural, etc.
Otherwise there would be no such thing as philosophy, which is an entirely respectable ally of science.
As well as reflecting on the Big Questions that stand behind science, philosophy reflects on matters of value -- it asks whether there are objective moral values, for example, and many practitioners reach the conclusion that there are objective moral values. And it helps us to refine what those values are.
So it can't be asserted without argument that in order to be fully reasonable, religion has to be established on the basis of evidence and scientific procedure. I think we can argue about religious values in a way similar to that in which we argue about, say, moral ones. And we can refine our (flawed)concept of god, just as Locke, Berkeley, Hume et al refined their flawed concepts of the external physical world. In other words we can reason about religious questions -- as very many philosophers do without the least temptation to rubbish it. And we can entertain the idea that through reason we can evolve the religious ideas that some of us have, that we can come to believe with good reason, and that we can refine our beliefs in pursuit of truth.