I think people often forget that science is a strategy, not an entity in the same way that religion is. At its core science is nothing but a system for collecting, interpreting, and understanding evidence with as little bias as possible. Human beings have many techniques, some informal and intuitive, for accomplishing the same thing. What makes science different is that it aims to be rigorous and adhere to logical principles in order to keep the amount of errors that arise as low as possible. Even the methodology of science is not set in stone, as we've learned about various psychological pitfalls that lead to inaccuracies (confirmation bias, memory fallibility, et cetera) science has changed in order to be more precise (by using double-blinded trials for example).
It's true that science can't disprove religious ideas, because science deals with inductive matters it can't really "prove" anything. It can however talk about statistical likelihoods, and make certain religious concepts extremely unlikely. For example, Jesus' resurrection. Science can't ask the question, "Did Jesus come back from the grave" because how would you go about studying that phenomenon? It can however ask, is it possible for human beings to come back from the grave? The answer is no based on study of human anatomy, hundreds of years of collected evidence, et cetera. Nearly every miracle mentioned by religion fails this test, which isn't that surprising given that's practically the definition of miracle to begin with.
Religion isn't exactly disproven by any of this, just made to be extremely unlikely. Which is why it's so baffling that despite all of the evidence gathered by our most reliable methods pointing in one direction, so many people point in the other. For example, 78% of the population of America is Christian despite the fact that the bible itself (the source of their religion) is a collection of books that was assembled at the request of a Roman Emperor (Constantine). And that doesn't even get into the fact that the document is full of historical accuracies, contains no corroborating evidence for any of its extraordinary claims, and has been sloppily translated numerous times.
Using the scientific approach the same way we do to answer any question (collect data, analyze it, then come to a conclusion with as little bias as possible) really doesn't reflect well on Christianity. Young Earth Creationists believe what they do for a very simple reason. One of the methods of science in testing a theory is to derive a "testable implication" from it, then to test that implication. Literal Christianity fails this test and biblical scholars did most of the legwork for us. They calculated the age of the Earth based on the biblical account, then the age (that testable implication) was shown to be false from geological evidence.
Saying that the bible isn't "literal truth" is just a way of coping with all of the factual inconsistencies and making everything so vague that it's difficult to know what is taken seriously and what isn't, so that more of these testable implications can't be derived, and thus disproven (inductively so anyway, we've already established it's not possible to truly disprove anything using induction). It's a defense mechanism.