A mendicant is a beggar. It is very ironic that the character, Mendicant, is rather arrogant and imperious. If you slavishly bow and kiss his feet, he will nonchalantly give you what you wish. If you try -- at all -- to stand head to head with him, he will demonstrate his superiority by cowing you into submission. I'm not privy to what went on between Mendicant and Julius, but I wouldn't be surprised if Julius refused to submit to Mendicant; that unwilling to sacrifice his dignity, he attempted some form (however timid) of posturing instead. In this light, Mendicant's actions make perfect sense -- although, this is all postulation, perhaps I've read him entirely wrong.
"Cult" makes it sound antiquated, however "reason" brings to mind the age of reason, which is more modern. So it does sound odd. I'm not familiar with it's tenets though, so I will not judge. For all I know, it' could be very clever.
From what I have heard about the Galvez family with diplomacy, it was likely that and more and I don't really doubt the insults or whatever else Noblesse claims related to negotiations with Barca oringinally.
