There's no principled way to choosing between a nearly endless number of unfalsifiable religious claims, or of persuading others to your way of thinking.

Sean, yes there is. First hand experience with the meaning of religious claims. Bypassing mentation, logic, and reason entirely.

Re-ligio - that means reunion. It is at core an inward-turned project of discovery of meaning beyond the senses of sight, sound, touch, etc. The world of experience in which we might care about such practicalities as "scientific falsifiability" is often of no interest to the happy sage, or only matters as the vivid echo of his own core of universal silence.