again, you're confusing MC with yourself. what you see, MC doesn't necessarily sees...
it seems you can't understand that concept.
players seeing Swordslaves approaching high order facilities doesn't mean anything for MC...
players watching Ren and Claire make deals doesn't do anything for MC...
and like I said, seeing that, even the players don't know how the high order and Ren framed the brotherhood, even if they know they work together.
the only way to know is choosing to help the high order stop the attack. and from there, you learn that they planted a sword in the storage room, and they can cloak items from sight and from emitting easily recognizable energy (not a single one of the brotherhood dark ones could sense the sword), which is very important information, and that the high order CAN pick up on that energy even from far away, even if it's cloaked, which opens up other hypothesis again.
MC isn't prepared to realize and actually think that Claire will betray him. but he has a big lead, that will be actual undeniable proof, that removes any doubt that Claire is the culprit.
sure, there might be no real positive or negative consequences for the player, but the different path and context will bring nuance to how things play out, and how MC has to deal with what is to come. the actual drama itself and its size.
Brotherhood holding a grudge only leads to small skirmishes and guerilla for revenge, that can easily be squashed.
High order is much more powerful, and can wipe out the brotherhood anytime. having a grudge means finding excuses at every opportunity to hurt them more or be more cruel.
you don't understand the balance of power here.
keeping the peace for the high order is only a front, appearances. they only need an excuse. Claire is actively working to create those excuses.
before Az went crazy, the high order seemed to be a decent organization. not saints by any measure, but "redeemable" in the context of the companion world, at least. it's only after the tragedy that everything went south for them.
so when you say "High Order faction has always been irredeemable", it's factually incorrect. they were a government sanctioned organization that worked to keep the peace and the balance of power, as well as hide companions and dark ones from the normal world. hunting down ferals, or criminals, preventing wars and large scale destruction... it's pretty "redeemable".