Acting like a real person is one thing. Expressing the sentiment that an entire race should go extinct is another. There are a lot of ways to be a believable, flawed human being without ever uttering a word about genocide. They could've had Kirk and the others be uneasy with the prospect of peace without taking it in such a racially oriented direction.
Kirks outburst wasnt to suggest genocide, Kirks response was to sit back and do nothing which is a whole other moral conundrum; do you help a mortal enemy in their hour of need? = the answer by the end of the film was a yes.
The only person who directly inferred genocide was West when he mentioned "cleaning their chronometers" and wipe them out.
End of the day Starfleet had been at a constant state of war with the Klingons since before this crew joined up, no wonder they would be jaded against them.