PFS Faction Traits

[Eilandor]

Hunter's Eye is a PFS Faction Trait (Andoran)

I am running the Reign of Winter AP (Not as PFS), can or should I allow the selection of that trait?

[Cao Phen]

Faction traits from PFS factions are under the "Pahfinder Lodge/Society" Campaign traits. Because the Reign of Winter has its own campaign traits, you can not choose those.

[SlimGauge]

Does the Pathfinder Society exist in your campaign ? If so, there's no harm in allowing the traits. If the Pathfinder Society doesn't exist, then if you want to use them, you'll have to reflavor them. Exactly how you do this depends on the trait in question and the organizations that are in your campaign.