This depends to some extent on the Christian involved. There are sects in the US, at least, that believe that God wants people to be rich and that God, therefore, approves of capitalism. A more mainstream approach to the issue emphasizes personal freedom and personal growth.
In this view, capitalism is compatible with Christianity because Christianity values the individual and wants the individual to develop his or her talents as fully as possible. People who adhere to this view can point to the parable of the talents as a support for the idea that people are supposed to improve on what they have been given.
Capitalism is the economic system that gives people the freest rein to develop themselves to the best of their abilities. They are not held back by tradition or by law. Christianity's reservations about capitalism are, in part, overcome by pointing this out.
Capitalism is the most explicit social reality of modernity, which is charaterized by individual freedom, progress, and reason. American Protestantism is also an essentially modern movement. In breaking with the Catholicism of the European traditions, American Protestantism was the first real social project of modernity that did not have immediate cultural ties to Medieval or even Ancient practice. This break resembles an ardent disdain for tradition (hence the contemporary Protestant emphasis on faith as opposed to tradition), and it fits seamlessly with the capitalist narrative of individual freedom.