It is an oft forgotten fact that Jesus was not a "Westerner" but rather, had an Eastern mindset, which is why he most frequently spoke in the form of parables. Westernized Christians, however, tend to read these stories literally, when they were always meant to be taken metaphorically. When we try to read and understand the Bible literally, especially the parables Jesus taught, it kills us and our religion becomes rigid.
The Apostle Peter was a rigid thinker and was stuck in his religious, literal thinking. How God handled him shows us that He does not give up on such people, but that instead, he will keep bringing the truth around again and again in different ways, until we understand it. In Peter's case, he instructed him, a devout Jew, to go to the house of Cornelius and to that of Simon, both Gentiles, and one, even a tanner. Jews were not to have any contact with the skins of dead animals, which was Simon's profession.
Peter didn't expect for God to "show up" at either house, just like some people never expect to see God anywhere outside their own religion. But Peter could not deny God's presence in both cases and ended up having a powerful connection and ministry to the very people he was originally so prejudiced against.
God has done the same in modern times to show us His existence and presence is not limited to Christianity, but many still refuse to see. How many Dalai Lama's will it take for us to know that God can speak through a Buddhist? How many Gandhi's before we realize God works through Hindus? Let us always remember that our religion is not God, only a "piece" of God.