Why do you think Indra, a chosen of Power, would be so offended and hellbent on revenge because Sylla ditched her duty to Memory ? Because Apostles share the same goals, and so do their chosen.
Maybe it's the human logic speaking, in contrast to "mysterious goals and ways" of apostles, but if they had the same goals, it would not be unusual for 3rd and 4th to work together. Maybe it's their way of bickering over details, dunno.
Also, hating on apostates isn't uncommon, even if you did not worship the god of the one that abandoned it's faith, even when from different religions altogether. Quite few examples of that through the ages, like vikings despising christians that left their faith for one reason or another, romans boiling alive some priests of greek gods that came over to worship their gods(xd for that one); even some christians, even though supposed to be all happy and all when new sheep joins the herd, were not always welcoming with open arms. Not the matter of being faithful in itself - the more zealous you are, the less it matters, and Indra seems to be turned up to eleven on zeal specifically.