However, on what basis does Copernicus have a problem with what [Christians] have done? Is there value to human life or isn't there? Is it wrong to take innocent life or isn't it?
Actions are not right or wrong independently of a moral code. Where that code comes from and how we justify it are the issues. One possible source for moral codes has always been our gods. That's why Hammurabi is depicted as receiving his code on a stone tablet from his god, and that is also why Moses got his from Yahweh on a stone tablet. Since at least the time of the Sumerian Empire, subsequent semitic nations followed that same paradigm, the Hebrew bedouins being no different. In fact, the relationship between Hammurabi's Code and the 10 commandments has been noted by scholars.
Killing is proscribed in the moral codes of most cultures, but that only makes sense. A society that prohibits murder is always going to be stronger and safer than one that allows it. The disappearance of human sacrifice (symbolized by Abraham's willingness to sacrifice his son) symbolizes an evolutionary event that took place in many human societies. Moral codes come from human societies, and society now benefits from centuries of evolution in our thinking about right and wrong behaviors. Wrong behavior weakens our chances of survival. Right behavior strengthens them.
Where I'm going with this is - objective moral values do exist. To compare humans to animals, a dog (namely mine) kills squirrels and chipmunks and feels absolutely no remorse over it. In fact, she clearly takes great pleasure in the act. Now, we do not consider her a psychopath and have not contemplated having her committed until she is no longer a threat to others. However, if she were a person who takes great pleasure in killing other people, it would be different situation.
Your dog, I must admit, is no more moral than Vice President Dick Cheney, who likes to kill birds and other small animals. He did express remorse for shooting his friend in the face.

There was a famous incident during the Carter administration where Jimmy Carter was out hunting in a boat. He spotted something in the water heading straight for the boat, panicked, and shot it. It turned out to be a rabbit, much to the hilarity of the press. I can think of few more moral men then former President Carter.
Most humans have built into them a respect for human life. Those few who don't are either locked up or bully their way into a leadership role with disasterous consequences. Different cultures define what is "innocent" in regards to defining "murder" but all cultures do condemn murder.
Indeed. Humans are not the only type of animal to have developed social behaviors. Lots of animals--insects no less--have evolved to embrace the principle of "strength in numbers". Like other animals, we have evolved instinctive behaviors to support and strengthen the group itself.
Using Hitler, for example. Most of Hitler's followers condoned what he was ordering be done to the Jews on the basis that the Jews did not deserve to live...
That's not quite true. I would say that most of his followers condoned the harsh treatment of Jews, and that played very well among Christians who had come to blame Jews for the death of Christ. However, Hitler's policy of extermination was kept secret precisely because the Nazis understood how far it crossed the line.
However, I can pretty much guarantee that they did not condone the same thing being done to their children or spouses. I haven't researched it, but I am pretty certain that prisons still existed in Germany during WWII and were used for Germans who committed atrocities against other Germans. So, while Hitler's followers found a way to justify the killing of Jews as "not murder," they did still condemn "legitimate murder," thus, the objective value of "murder is wrong" did remain intact during WWII Germany...
Hypocrisy is nothing new in humans. However, it is important to remember that most Germans did not know the full details of the extermination program, just as most Americans do not know what happens to muslim prisoners. Many still openly condone the torture of suspected terrorists, while others find ways to pretend the brutal policies are not real torture.
Granted, it was twisted and distorted, but the people involved were able to maintain the idea that they were not murderers. Why was that important to them? Because without that justification, they would have become murderers in their own eyes. All humans have built into them the idea that murder is wrong. Whether one believes in the Law-Giver or not, all have the law in them.
I agree with you on that conclusion, but we may disagree on where the instinct comes from. I think that it comes from many generations of messy trial-and-error behavior. Eventually, those humans with a heightened sense of empathy and altruism came to form more stable societies. There is a good reason why that kind of behavior should have evolved in us. Now our problem is overpopulation. By valuing life so highly, our own success at staving off death and being "fruitful" threatens our future survival.