They were not to vex (to treat violently) a stranger (a temporary inhabitant) nor oppress them - The children of Israel were to remember how they were treated when they were strangers in the land of Egypt and not treat a stranger in the same way . . . strangers were temporary inhabitants
One manner of law - the whole context is concerning blasphemy - so the law was that when one blasphemed the name of the Lord they were to be put to death - this was for the Israelite as well as for the stranger - the temporary inhabitant and yes that is carried over into the NT - Matt. 12:31,32
Romans 10:12 - There is NO DIFFERENCE between the Jew and the Greek - 1 Cor. 12:13 For by one Spirit are we all baptised into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit. - Galatians 3:28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all ONE in Christ Jesus. . . .
In the NT - we do not keep separating Jew and Gentile, bond and free, even male and female because we are ONE. So when God looks upon the members of the body - he sees Christ's body - He doesn't see Jew, Gentile, male, female, bond, free - We are all the same in the body of Christ. Wouldn't you think that to keep making a distinction, when God no longer sees a distinction, is wrong?
NOW . . . . you are NO MORE STRANGERS AND FOREIGNERS, but fellowcitizens with the saints and of the household of God; And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;