At this point, no it isn't the cause of world conflict. World conflict right now is more who controls the resources, rather than the amount of resources used. Yes, you can say that China's industrialization has driven up prices of raw materials, but they'll make it to a post industrial economy eventually.
I agree that most Western nations are at a point now where replacement rates are just maintaining the population. People are having less kids these days, plain and simple. The brunt of the world's population can be found in China and India, obviously. Combined they make up 2.54 billion people or roughly 37% of the world's 6.91 billion people. The US on the other hand only makes up 4.5% of the world's population at number three and the percentages go down and down as you make your way down the list.
If China didn't control so many resources, I could careless about how big their population gets. Yet they do control many vital resources and needless to say, those 1.3 billion people will use such resources rather quickly, regardless of lifestyle.