How does one even begin to address outrageous statements as this?

Start by removing emotion from your analysis of the statement as well as hyperbole. If you have a strong opinion on a topic is is difficult to use reason effectively, since emotion gets in the way. Then, look at the claim being made and to the degree it is being made—specifically look for absolute terms. In this case, the degree is "much" which is difficult to define. I don't think anyone would argue with the statement

Belief in "the one true religion" is at the heart of some of the violence, killing, and oppression that has been committed throughout the centuries.

So this is a discussion of degree. I would ask the person who said/wrote this, to quantify "much" then take the argument from there. Their understanding of "much" might be in-line with your understanding of "some" and you just might agree with each other.

You could also say confusing cause and effect.
Simply put, history is written by people and opinions is, or could have been, interjected when it comes to actual motivation. It cannot be proven why someone was truly motivated to commit an act in its entirety. An example I always use is one of the inquisitions, sorry forget which one and I'm lazy. But as the history of it unfolded the perpetrators of the deaths of those people evolved into the following concession. "If you leave your wealth, property, belongings, etc. behind you, you will be allowed to leave our "kingdom ,society, whatever" without recourse. This seems to point to their religious beliefs as not being the actual motivation for killing people who would profess different religious ideas in public. I'm of course not arguing that I know the actual motivation was greed, but there is an argument for it being at the core possibly. In other words, believe what we want you to believe so you will not be killed because if you die you cannot gain possessions and in turn we cannot confiscate some of those possessions. What's the motivation? The killing might have been merely a scare tactic and greed and gaining wealth for the few in power was the motivation. Just an alternate theory or approach.