Can history-centrism cause some religion or the other to be belief-based? The notion of “history-centrism” is too vague to allow a serious answer. In so far as this refers to a “Grand narrative”, and this narrative is either an oral or a written account, it is a candidate for the status of ‘belief’. Consequently, your question takes the following form: Does “believing in” the truth of some or another historical event cause a religion to base itself on “beliefs”? (The contrast term to “belief” will have to be attitude or action or event.) As Christians do, you might want to distinguish between “believing in” (a propositional attitude) and a set of “beliefs” (which are a set of propositions). In that case, the Christian stance is superior to your formulation: they say that believing in God is primary with respect to the belief that “God exists” or that “Christ has come” or any such thing.
Empirically speaking, has history-centrism caused some or another religion to be belief-based? An answer to this interpretation of your question depends on how you write history and whether one sees historical consciousness as a prerequisite for believing that some proposition is true. Frankly, I cannot quite see how such an epistemological claim (the latter part of the above sentence is an epistemological claim) can be argued.