Kirk's morals are a set of words and actions imposed on him. They are not part of his character. The Kirk in the parallel universe had learned other words and actions. Though the mirror Spock has integrity and the mirror McCoy humanity, the mirror Kirk is (or was; he must be dead by now) a thorough going rat. The only redeeming quality in either Kirk is a deep-hidden humanity that occasionally, unexpectedly, surfaces. When it does, it's like finding a diamond ring at a beach.
Fortunately, 'our' Kirk lives in a less repellent society and obeys its laws. And he has Spock for a logical conscience and McCoy as a humane conscience.