Myth:
Most instances of so-called "religious violence" are really just examples of political or social violence cloaked in religion. There are, therefore, not really religious violence in the first place and atheists are wrong to criticize religion because of them.
Response:
The large amount of religious and religion-fueled violence in the world today and throughout history creates a serious problem for religious believers: how can they claim that their religion is a source for morality and social order when so many people are killed in its name? One tactic is to claim that many examples of "religious" violence are not in fact about religion at all. The blame lies with politics, nationalism, economics, and other factors. Religion is thus cleared of any blame.
To be fair, it is common for conflicts to involve a number of different factors. Political disputes, economic disputes, and even ethnic disputes are often a part of whatever is going on, not just religion. Given how tightly integrated religion is in most cultures, it would be unlikely to ever find a "pure" religious dispute that is broad enough to lead to extremism, violence, and war. We should expect that however religious a conflict is, other factors will be drawn in and perhaps play important roles.
This, however, is a major reason why it's difficult to give much credit to the above attempt to deflect atheists' criticism of religion by denying that religion is really involved in such conflicts. If there are pretty much always a variety of factors involved in any dispute, that can't cause us to concluded that a violent conflict isn't "really" religious. This is a testimony to the complexities of human culture and motivations, not to any essential peacefulness of religion.
What matters is not so much whether religion is a primary or even the sole factor, but whether religion is providing a primary motivation or justification for people's violent behavior, rhetoric, ideology, etc. Economics might be an important factor, for example, but it's probably not legitimate to call something an "economic" conflict unless people are consciously and deliberately pushing economic advantage as the purpose for fighting. Are citizens called upon to join the fight, for example, in order to promote the nation's economic health? In such cases, the removal of economics would also mean removing the justification people have they might be able to find another one, but that would significantly change the tenor and nature of the conflict.
The same should be considered true for religion as well. Even if religion is not really a primary factor, it can legitimately be called a "religious" conflict if religion is providing the primary explanations, justifications, and motivations which the bulk of those involved actually use. The existence of other factors means that the removal of religion might not end the conflict, but the removal of the primary justifications and explanations would have to make significant changes in how the conflict is understood and pursued, not to mention its ultimate goals.
For example, some like to claim that the Israeli-Palestinian conflict is not "really" religious, but is instead a conflict over the control of land: both Palestinians and Israelis want it. It is claimed that the conflict would be basically the same without the involvement of religion, but that strikes me as an almost deliberate refusal to acknowledge religion's role here. When it comes to Jerusalem, for example, various groups are willing to fight for control precisely because of its religious significance you don't see the same zealous fervor over other cities.
Religions have effectively created an artificial scarcity by declaring very limited tracts of land to not just be holy, but in fact the holiest territory in the world. Possession and control of such land cannot be compromised on, cannot be negotiated away, and certainly cannot be compensated by providing different land. People want this land not only for religious reasons, but those religious reasons create the most passionate and uncompromising fervor.
The belief that God has given this land to a people creates an explanation for why they are there, a justification for using violence to defend it, and reason for never even contemplating the possibility of compromise. Without the involvement of religion, it's possible that the dispute might have been settled already because people wouldn't believe that compromise and negotiation would be a sin against God's plans.
The same is true in other conflicts where religion is an issue: religion provides an explanation for why people are in a certain position and/or having certain problems; religion provides a justification for asserting certain authority or power over others, over land, etc.; religion provides a reason for using violence; most of all, though, religion creates a basis for refusing to ever negotiate, compromise, or give in to the desires of others. When religion is involved in a conflict in this manner, it's unfair and incorrect to refuse to describe it as fundamentally religious.
Even if the conflict would continue on some level without religion, precisely the removal of religion would remove many of the most significant impediments to a peaceful resolution. Removal of religion as a factor would, then, make it easier to end the conflict entirely. If that doesn't make the conflict basically religious, what does?

