Problem being, the Salt Vampire was killing just for the sake of killing.
The humanoids on Taurus Two were killing just to kill yet Spock recognized a duty to alien lifeforms even when proven hostile. The salt vampire was minimally no different.
It obviously wasn't starving to death when it killed the first two members of Kirk's landing party.
You don't know if the lifeform was hungry or not or fearful of discovery and extinction. Kirk and party made no effort to understand the lifeform or what motivated her/him. Risk is their business and they are to seek out new life and new civilizations yet here they go straight to the nuclear option of extinguishing the last of the indigenous life.
They put down a rabid dog, and I've never had a problem with it within the context of the Star Trek universe. What kind of life would it have had if it couldn't control itself? As an exhibit at some Federation zoo?
It wasn't "rabid." It was a lifeform desperate to survive. If Kirk and crew had at least made an attempt to reach out and it failed that's one thing, but not to have tried at all or even given a peaceful solution any consideration was immoral.
Possibly the Chief Medical Officer has more latitude, since he is outside the chain of command? We never saw McCoy have any issues with challenging Kirk or anyone else in command.
True, Kirk & Spock may give McCoy a bit more latitude, however, that doesn't explain why they drummed out a black man and kept a white man who did the exact thing (possibly worse).