I admit there seems to be a disconnect between the feelings towards Klingons between TFF and TUC: they were okay throwing back a few alien beverages with them, but when their moon blew up, well then "let them die!" Still, I believe the prejudice existent in ST VI is actually pretty realistic. As pointed out, the Enterprise had had several very negative run-ins with the Klingons over the years, and it seemed as if the two cultures could never coexist. They were almost seemingly "varelse" (to quote another of my favorite sci-fi storylines), and it was hard for the Enterprise to believe they could be "raman".
Think about yourselves. Each of us has been thoroughly taught not to feel racial prejudice. But if most of us were honest, we still retain quite of bit, though we try to suppress it. Our prejudice may even be directed towards our own race, such as the prevalent "wisdom" that only whites are capable of racist actions. Even if we have kept our racism in check, how often do we maintain other prejudice: sexism ("men are babies", "women are terrible drivers"), ageism ("old fart driver"), political prejudice against different ideologies and their motives, different religions (or anti-religion in general, or anti-atheist), professions, people with disabilities, the rich, the poor, and on and on and on.
If we are honest, we are prejudiced towards one group or another. We can afford to be understanding and even appreciate the humanity of Kirk and crew, as it truly represents our species and our imperfection. Yet in the end, it was the bigoted Kirk and his friends who stopped the assassination and guaranteed peace between the two peoples. That's something we can all learn: even if we are prone to bigotry, we are also capable of choosing to be better than that.