This is a much more thoughtful treatment of the issue!

By "razing of the Incas" I mean the overthrow of the Incan empire and looting of valuables to Spain, not the accidental introduction of disease that killed most of the population. The Incas themselves were no saints, which is why the mechanism of "rouse the surrounding peoples to help us conquer the empire" worked; the question is just about what kind of atrocity has been committed in the name of, and by those who identify with, Christianity.

It's quite true that all the examples I gave were Catholic.

However, you can't reasonably say, "Well, this was politics/imperialism not true Christianity" as a defense against atrocities committed by Christians and not use the same reasoning on, for example, what communist countries did.

So if that's your defense, I think your attack on "nothing like the atheistic atrocities" is still incorrect.

And anyway, Protestant Christianity was used to excuse and motivate its additional atrocities, like continuing the slave trade and continuing the institution of slavery (yes, I know that abolitionists also usually appealed to Christianity to support their points--everyone was Christian, mostly Protestant, in the U.S., so what else is there to lean on?); the repeated annexation, often violent, of North American native lands; the pogroms against Jews in Eastern Europe and Russian in the 1800s (Orthodox, not Catholic); New England witch hunts; the anti-Balaka militias in the Central African Republic ten years ago, and so on. Some of these rise to the same general level of horror, or possibly surpass that, of what Communist revolutions and subsequent authoritarian regimes have inflicted.

In every case, you can find Christians also objecting to the actions. And you could find a lot of atheists objecting to Communist violence. And you can find people of other beliefs also committing violence, and others of those beliefs objecting to violence. So I still don't see your "nothing like the atheistic atrocities" statement as historically justified.

If you wanted only to claim that atheism isn't a panacea against atrocity, then pointing at, say, Stalin would justify the claim.

If one wanted to make a better/worse comparison, that would be tough to make convincing.