How's "render unto Caesar" particularly relevant here?

(Leaving aside the point that "render unto Caesar what belongs to Caesar" served to neatly sidestep the trick question that evoked the words.)
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Muslims argue about a lot of things, but they don't get into arguments about who is a Muslim and who isn't

They do actually - for example, one of the elements in the present trouble in Syria is that the Alawite sect, to which the ruling regime is associated, should be counted as Muslims or pagans.