The Scions do teach the Warrior of Light a few things, though arguably those might not be strictly Sharlayan. Such as the workings of aether back in the 2.X series. However you cannot deny granting the Warrior of Light access to Matoya's research on Aetheric Convergence, as well as the Anti-Tower of all places, certainly constitutes sharing Sharlayan knowledge with an outsider.
The difference between Ishgardian Astrologians and Sharlayan Astrologians primarily seems to be that the Ishgardian Astrologians focus on reading the stars to predict the future and completely ignore the magical aspect. If I'm remembering the quests correctly, the magical aspect was deemed borderline heretical because it did not come from Ishgard. That's another reason it was vastly unpopular amongst Ishgardians when Jannequinard kept trying to introduce it to Ishgard because of the good it could do.
That said, it seems to be the Bibliothecs who are against sharing knowledge with outsiders, particularly any knowledge with tangible affects on history, like magical knowledge. The Sons of Saint Coinach are another group of Sharlayans who do not seem to have an issue working with non-Sharlayans, though that seems to be less a case of them sharing specifically Sharlayan knowledge, and more them sharing knowledge about the Allagans they've uncovered.
I mean, put it this way. If the Sharlayans as a whole were dead-set against using their knowledge to assist other nations, then the Aetheryte Networks would've never been constructed.
The difference between Ishgardian Astrologians and Sharlayan Astrologians primarily seems to be that the Ishgardian Astrologians focus on reading the stars to predict the future and completely ignore the magical aspect. If I'm remembering the quests correctly, the magical aspect was deemed borderline heretical because it did not come from Ishgard. That's another reason it was vastly unpopular amongst Ishgardians when Jannequinard kept trying to introduce it to Ishgard because of the good it could do.
That said, it seems to be the Bibliothecs who are against sharing knowledge with outsiders, particularly any knowledge with tangible affects on history, like magical knowledge. The Sons of Saint Coinach are another group of Sharlayans who do not seem to have an issue working with non-Sharlayans, though that seems to be less a case of them sharing specifically Sharlayan knowledge, and more them sharing knowledge about the Allagans they've uncovered.
I mean, put it this way. If the Sharlayans as a whole were dead-set against using their knowledge to assist other nations, then the Aetheryte Networks would've never been constructed.