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".
I don't know if it's writer's additions or originally planned, but in the novelization starts starts out with attacks on Federation outposts by Klingon renegades i.e Chang. One of those put Carol Marcus in hospital with critical injuries.
Factor that in and some of the attitudes by Kirk and Co become more understandable.