In Matthew 6: 32 ("For all these things the Gentiles seek.") it seems as if Jesus divided the world into gentiles and non-gentiles. Who were the non-gentiles implied in the verse?
A gentile is anyone who is a non-Jew. That's the standard definition. So the "non-gentiles" are the Jews. There's really not much more to it than that.
As for the relevance: The Jews (Israelites) worshiped the true God of Abraham, Isaac, and Jacob in contrast with the Gentiles, who sought after other gods.
If you look at the versus surrounding 6:32 you see that Jesus is trying to use illustrations to get his point across. If you read down from versus 19-34 You can see that he is trying to teach the Christians then to focus on the preaching and teaching work instead of material things they need. Matthew 6:33-34
Jesus is in effect telling them that they don't have to worry about food, shelter, clothing, and such because god knows that you need them and will provide. He was also talking about how the gentiles sought after riches, fame, and positions of power. He was warning them that a man cannot slave for 2 masters Matthew 6:24 or that is that they couldn't try and gain fame and fortune and still devote their time to serving god.
He illustrates with lesser thing such as birds and vegetation of the field. Those lesser things are taken care of, but yet how much more so for his people will he make sure they are taken care of? Matthew 6:25-32