First, I searched 'Adopted' and got several threads confirming my initial understanding of the trait. I then searched Enlightened Warrior, and while I think I understand what was said, I need some further clarification. I would like to quote a Pathfinder approved text/site/whatever to show I've done my due diligence on the matter.
Adopted:
You were adopted and raised by someone not of your race, and raised in a society not your own.
Benefit: As a result, you picked up a race trait from your adoptive parents and society, and may immediately select a race trait from your adoptive parents' race.
Okay Adopted works for Race traits, not Racial. Got it, no problem.
Enlightened Warrior:
The following are race traits for idyllkin.
Enlightened Warrior: You have always found it easy to
maintain inner peace and enlightenment that translate
well to the battlefield. You may take levels in monk even
while maintaining a neutral or neutral good alignment.
Therefore you need to be an idyllkin to take this race trait.
I cannot find anywhere in the Pathfinder Player's Companion: Blood of Angels that this is a heritage feat.
Therefore, are you allowed by RAW and RAI to use Adopted to choose the Enlightened Warrior trait?
TL;DR Can you use Adopted to pick the race trait Enlightened Warrior?
I would say that's pretty much exactly what Adapted is for.
