Re: STVI without the racism
It's the ST5 Klingon character of General Korrd that represents something of a discontinuity, as the old wardog seems to have Kirk's sympathies and vice versa. But that's individual Klingons, and while Korrd may actually be a fairly typical example of Klingons of his age and position, the mass of young hotheads that Kirk would typically deal with would outweigh even the portly General!
I always attributed Kirk's sympathy to two things:
1. His recent demotion to captain and reassignment to Enterprise.
He got what he wanted but likely thought about what might have happened had things gone down differently in TVH.
2. Korrd's military strategies were required reading at the Academy. A young Kirk not yet jaded by numerous run-ins with the Klingons may have admired the general's intellect and leadership qualities and seen him as the type of commander he wanted to be like (within the confines of Starfleet regulations, of course).
"He clapped his captain—his friend—on the shoulder. Yes, this man was very much like James Kirk, in all the ways that mattered." --Christopher L. Bennett-- Star Trek: Mere Anarachy, The Darkness Drops Again