In your opinion, are these feats
a Ranger's attempt at imitating a deity they like,
or
a power granted by deities, similar to cleric spells
?
The book (inner sea combat) doesn't really explain how it works, and it's GM fiat; so if you were the GM, how would you explain it?
Could be either, could be neither, I imagine - it seems like that'd be up to a player to decide for their character. As for me, I'd always imagined it as an effect of being raised in a particular faith's culture or beliefs, and that set of habits and values coming out in how they choose to fight.
If you're asking to know whether or not the ranger would lose those feats if they transgressed against their deity....no is my answer. They would lose spells, and maybe some other class features that might be supernatural, but even that isn't really supported. A ranger is not like a cleric or paladin, their powers aren't much linked to a deity. I think the feats represent being active in that faith and having learned from them.
The book does say you need to be of the matching faith to recieve the combat style, but ex faithful should be fine.