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.
Gill's Exposition of the Entire Bible
For after all these things do the Gentiles seek,.... Or "the nations of the world", as in Luke 12:30. The Syriac reads it so here: the phrase, "the nations of the world", is used of the Gentiles, in distinction from the Israelites, thousands of times in the Jewish writings; it would be endless to give instances. These knew not God, nor acknowledged his providence; the greater part of them thought, that the soul perished with the body; few of them thought, that anything remained after death; and they that did, spoke very doubtfully of it: wherefore it is no wonder, that such persons should greedily seek after, and be anxiously concerned for all these things, food, raiment, and riches, and a great plenty of them; since this is all the happiness they expect; and imagine, that this is to be acquired by their care, thought, diligence, and industry; having no regard to a superior being, and his all wise providence: but for the Jews, and so Christians, who have a divine revelation, the knowledge of God, and his providence, and of a future state after this life, to act the same part the Heathens do, is exceedingly unbecoming, absurd, and wicked: and besides, such greedy desires, immoderate care, and anxious solicitude, are altogether unnecessary;
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