Religious “knowledge” is based around non-falsifiability of certain doctrines and axioms. Even within their own epistemological frameworks they have non-falsifiable arguments.
Agreed! Vaguely. I'm not sure I'm sure of that - but only because I personally just don't know enough religion to confirm.
...scientific process which must be fundamentally falsifiable.
Disagreed, following on from Kuhn and Lakatos (not exactly a high-quality source, but it's a reasonably to the point overview of the criticisms of falsifiability).
In a broadly over-general way, people who adhere to both science and religion attempt to make sense of their experiences as everyday practice. Both lay-persons and experts (across both science and religion) attempt to mobilize what they understand as the shared practices by which valid knowledge is produced. Those shared practices can be different across science and religion - but not always, note the adherence to formal academic practices and traditions among Western religious experts, and the study of religion in academia - but they are both epistemic practices differently structured, if often incommensurable.