I think it helps that, at least in my opinion, the Space Marines know better who the Emperor actually was (a super-psyker) and with their ludicrously challenging training, they are willing to allow certain "abnormalities" other Imperials wouldn't tolerate to stand, since they did survive to Neophytehood. Sure, some Space Marines are as leery of psykers as the next GE-fearing Human, and the Black Templars are a Chapter of witch-watching puritans, but I think Space Marines in general, not being so weighed down by the Imperial Dogma, can see past the blanket "psykers are bad!" that the Ecclesiarchy preaches, just like many Inquisitors, and other very powerful, more in-touch with the real universe people are, can more readily gauge a person for who they are and what they do, rather than one trait they were born with. Hell, half of being a Space Marine is gaining new traits you weren't born with, and if they can tolerate flesh-eating, blood-drinking, and slowly turning Crinos werewolf Space Marines (since the Blood Angels and Space Wolves are so popular they can't be in the "regular SM Codex), it seems that something as little as psychic powers, especially known about powers, so you have been tested, and are being watched, would be no biggie.
Still, having a Librarian also be a Chaplain seems a bit much. Agreed, the watchers shouldn't also need watching. That said, and no they aren't typical, the Grey Knights have every type of Marine in their army, so they must have Chaplains, along with all being psykers. Still, this should be the exception, not the norm.