There is no such thing as objective morality. Murder is defined as immoral killing, therefore murder is always immoral. Vegetarians think it's immoral to kill animals, but not everyone agrees. Some people think abortion is murder, but not everyone agrees. And some people think it's okay to kill in the name of a god, but most people wouldn't agree. To answer your question: Yes, a murderer who thinks his killing is justified should still be punished. By "punished", I assume you mean imprisoned. If that person is a threat to society, he should be detained.
