Is the MC oblivious to the to the cheating throughout the entire game in Shadowcore?
Yes. Mist never found out about Brad fucking Elisha behind his back (and Elisha being a slut in general) except during one of the bad ending (Slave Market ending specifically, where Brad bought Elisha and, instead of resuming their adventure, took Elisha - who's more than happy - away as his woman while telling him how they always have fucked with Mist unknowing the whole journey).
Well, during one of the penultimate fight, the main antagonist (Claude, the masked Demon King's former general) used the book Memoria to unlock Mist's memories and shown him that, unlike his initial fake memories in which he's always have and always been Elisha's childhood friend, and Elisha's a thorough virgin who never knew anything about man, the truth is Elisha's been fucked regularly during what's supposed to be his village's "secret ritula in which only chosen people may attend to Elisha and help her duties as the priestess".
But even then, he only knew that 'Elisha got fucked by the village guys', not 'She's been whoring herself out and getting fucked regularly by the mercenary old man all these times'.