Certainly not behavior that should be allowed for on-duty soldiers (and it isn't, the article confirms that much) but I don't see this as a terrible travesty or anything. As long as nobody is being forced to embrace Christianity it's no big deal even if it's inappropriate.
the way it's depicted in the article is extremely damaging to the mission: Iraqis will resent the US presence in the region even more if they feel American troops are trying to push Christinity on them.
I don't disagree with that, I just think the Iraqis in the article are making a bigger deal of this than they rationally should be. But it's a religious issue, so I guess rationality is a bit too much to ask.
Their culture, for better or for worse, doesn't especially shine on Christian evangelization. It's hypocritical, but so are most arch-religious societies. If we are going to practice cultural sensitivity, not doing this would be a good place to start.