(Small disclaimer, I'm only halfway through Assassin's Fate, which is why I'm writing this on the internet and not having it set in stone. Also, no spoilers for AF please!)
I think the reason Fitz can never quite forgive and start to trust Rosemary is because his view on morals was taught to him by Chade (intentionally) and Burrich (passing on his own world view). He wasn't thaught to differentiate between right and wrong and to act after that, he was thaught that loyalty to the Farseer crown was The right, thing period. He isn't supposed to protect the king because the king is a good person who helps people, he has to protect the king because that's his duty. Because he took an oath. When he was eight.
You know. Around the same age Rosemary was when Regal manipulated her into giving him information about Kettricken.
His belief in the Farseer crown never waivers. He can never even consider if another ruler/political system would be better for the citizens' wellbeing. He does care about people, deeply, and wants them to be safe and happy, but in his eyes, the only way he can achieve that is by making sure the monarch is safe.
Rosemary's fault was trusting a charismatic leader when she was just a kid. She didn't realize Regal was using the information to hurt Kettricken. She grew up and learnt Regal's true intentions and lost all loyalty she had felt to him. In Fitz's eyes this makes her twice a traitor, she betrayed Kettricken AND changed who she was loyal to. He can't fathom that being for anything other than personal gain, the leader's character doesn't change the fact that betrayal is wrong. Oaths have to be kept, even if they were made by a child who didn't know better. It is such a fundamental part of his worldview that everything would completely fall apart without it.
