There were not formal "caste" systems in Jesus' time but certainly there was, even as in our own society, a "class" system. There were the rich and the poor. Poor labourers and wealthy merchants. There was the ruling class of occupying Roman officers and governors. There was the so-called "king", Herod and his wealthy court. There were religious classes: the poor and uneducated; the scribes, Pharisees, and Sadducees, most of whom despised the spiritually "unlearned". Women as an entire gender were considered, for the most part, little more than the possessions of their fathers and husbands. Lower than women in social status were the slaves who really were the property of their wealthy owners. Finally, at the bottom of the ladder, as far as the Jews were concerned, were the tax collectors. Not only were tax collectors greedy and oppressive, gaining their wealth at the expense of their brethren but they were seen to be traitors who collaborated with the Roman occupation.
To the majority of Jews in Jesus' day, Gentiles were despised. Any Jew coming into close contact with Gentiles considered himself "unclean".
A follower of Jesus must set aside all such biases. As the Apostle Paul put it:
Galatians 3:26-29 [NLT] For you are all children of God through faith in Christ Jesus. 27 And all who have been united with Christ in baptism have put on Christ, like putting on new clothes. 28 There is no longer Jew or Gentile, slave or free, male and female. For you are all one in Christ Jesus. 29 And now that you belong to Christ, you are the true children of Abraham. You are his heirs, and God's promise to Abraham belongs to you.
I hope you have found this helpful.