The scientific method arose from Christendom in large part because Christianity holds that a rational god created a rational universe which is understandable;
It also arose in the Middle-East during the Islamic Golden Age for much the same reasons (but with 'Christian' and 'Christianity' replaced with 'Muslim' and 'Islam'). This is a curio of the scientific method's historical development, as is, say, its geographical origins (in the West rather than the East, and for good reasons).
But saying that this makes science a subset of
religious philosophy, and specifically
Christian philosophy, is a
non sequitur - it does not follow. Science is no more a distinct subordinate to religious philosophy any more than it is subordinate to Western philosophy - it come from thinking done in Christendom, but it makes no Christian presuppositions, it makes no foundational assumption that Jesus was God incarnate and died for our sins (etc).
Indeed, its historical roots happen to run through Ancient Greece as much as Christendom; does this mean that modern science is necessarily and inextricably within the domain of Zeus? Of course not.
science rests on philosophical presuppositions that are not scientifically verifiable.
Certainly: it rests on presuppositions like "1 + 1 = 2" and, more fundamentally, the axiomatic foundation of logic and mathematics.
So it's not reasonable to propose that there can be such a thing as knowledge that arises out of scientific (but not religious) methodology, in a way similar to the fact that it's not reasonable to hold that there can be a tree growing in Kansas that is not also growing in North America.
Sadly, it doesn't follow that nested hierarchy.
To say that it is, is to say that I am Jewish by virtue of being born in the UK - after all, my culture is indelibly linked to its Christian history, which is itself rather heavily based on the Christian religion (in its various incarnations - Catholicism, Protestantism, etc), which is itself a follow-up to Judaism. Therefore, since these monikers are apparently inherited, I am Jewish because the culture of the place of my birth happens to run through Jewish history.
But British culture is also profoundly influenced by Russian history and culture, so that means I must be Russian too!
And just like that, I'm an Anglo-Russian Jew. Oj vey!
(If you think my logic is flawed, then yours is too. PROTIP: Monikers don't operate under the transitive property).