Who were the non-gentiles implied in Matthew 6: 32? 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;