Some people refer to Kirk and his statements in TUC as racist. But are they? His "let them die" might be the result of years of observing the Klingons in action, and simply wishing the the whole thing to be over with.
I think Kirk was "acting out" as much as anything else. There was the death of his son at Klingon hands (which he clearly still had issues about - who can blame him?), Spock's sudden bombshell, impending retirement (which would have made for a ... less than even emotional state anyhow), and possibly other occurrances that all led to him speaking in haste and anger.
Certainly, Kirk had absolutely no reason whatsoever to LIKE Klingons, but his attitude in TOS was .... much more tolerant. He might have had no hesitation in fighting Klingons then, but I always thought that he'd have baulked at causing or allowing their outright extinction. The Kirk seen early in TUC was, for me, very disturbing.
Then again ...
Someone who has defended the Federation for most of their life, could be forgiven for looking upon the major misfortunes of his (perceived) foes as A Very Good Thing. Certainly, there was at least one person at that meeting who had much worse thoughts.