Shit, tons of religious people don't know much about their own religion.

Yeah exactly. And considering clerics are devotees of specific deities it’s not like they’re going to be experts outside of it. As a DM I assume clerics have a firm understanding of their god. You don’t have to roll to know anything I expect an ordained minister to understand about them. But just like I don’t expect a priest of Iuppiter to understand Cybellian rites or Saturnian prayers you’re shit out of luck about questions not relating to your god.

And in that vein basic questions about local religion should have a low dc, but cultural distance can increase it. That priest of Iuppiter may have reason to know about other deities in their region even secret ones, but knowing jack shit about Shiva is academic to them. Knowing anything about Zoroastrianism is on par with knowing history to them. They likely know a bit about Ra and Osiris, but only because those are basic facts about a significant nearby culture’s religion.

All the advantages that being a cleric provides here should be represented in the form of proficiency. But you aren’t studying this shit, you’re deepening your connection to your deity.

That said I do think there’s room for an int based holy caster in something like pf2. A religious scholar rather than cleric

Yeah, like the proficiency represents training and study, but an Int (religion) check usually involves knowledge of deities, mythology or symbology. That said, you might rule that a practical application of that knowledge, such as how to perform ceremonial rites, might constitute a Wisdom or Charisma check instead.

The issue isn't really there, but that it's also the check for knowing about your own religion.

DMs: if a character wants to know something about their own religion, a good solution to this is to just tell them, rather than requiring a check (or if you want the group to make checks for something obscure, give a bonus or a lowered DC to someone if they're a member of that faith.)