There are two belief systems called science.
The less common one is the one you outline immediately after denying its existence: it's about asking questions and trying to establish evidence-based models to make predictions and testing/validating the assumptions in those models. It's probably more accurate to call this belief system empiricism.
The more common one is a deferral to expert authority, where experts are designated by certain established scientific institutions. Because many lack the time/will/ability to independently verify claims made by authoritative figures, this deferral requires substantial trust in these institutions to come up with good answers.
This second belief system is what most people mean when they label themselves or others as pro- or anti-science. Paradoxically, even though the authoritative institutions ostensibly produce information empirically, expressing skepticism and asking questions is often perceived as a lack of faith, and therefore anti-science.