Terms and Definitions:
Gentile: A biblical term for a non-Jewish person.
Circumcision: A ritual act that was often used to mean someone who has become Jewish.
Jerusalem Council: A gathering of early church leaders to decide the question of whether gentiles must become circumcised to be saved.
Are Both Jews and Also Christians Obligated to Keep The Law of Moses?
This is a complicated and sensitive topic, and is perhaps one of the oldest debated topics in the New Testament. The topic was at the very center of debate in the Book of Acts chapter 15, in an event which we have come to know as "The Jerusalem Council". The answer that the disciples of Jesus concluded can be found in these verses:
[Act 15:18-21 KJV] 18 Known unto God are all his works from the beginning of the world. 19 Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God: 20 But that we write unto them, that they abstain from pollutions of idols, and [from] fornication, and [from] things strangled, and [from] blood. 21 For Moses of old time hath in every city them that preach him, being read in the synagogues every sabbath day.
Now it's important to understand a few things from this chapter. First of all, the purpose for the "Council" was to answer the question of whether a Gentile (a biblical term meaning a non-jewish person) should have to get circumcised and keep the law of Moses. (Circumcision is a ritual act whereby someone becomes Jewish in this usage,) It was never even a question whether a Jewish person would be obligated to keep the Law of moses at this council, as it was already assumed they should. This means that all the disciples of Jesus (who were born Jewish) would have been still keeping the law, even after Jesus ascended to heaven. Again, the only question here was if a gentile would have to keep it too.
The answer appears on the surface that the gentiles would only have to do 4 things:
Not worship Idols.
Not commit Sexual Immorality.
Not eat food that died improperly (here called strangulation).
Not eat blood.
Now here is what is interesting. These 4 things are found in the Law of Moses, in a section known as the "Heart of the Torah" in Leviticus chapters 17 and 18. If the law was done away with, then why is the Jerusalem council referencing the Law? Specifically, the laws here pertain to gentiles who are living and conducting themselves in and among the Jews. The Law does not allow Jews to be around or associate with gentiles who do any of these 4 things.
But why only these 4 things? why not rules such as do not murder, or steal, or lie? Notice what it says in the last part of the verses above: "For Moses of old time hath in every city them that preach him, being read in the synagogues every sabbath day."
You see, since per the law, Jews are not allowed to be around any gentile who commits any of these 4 acts, then gentiles doing these things would be very problematic for jews if they were to go to a synogogue. Therefore if the gentiles wanted to learn the ways of God and the law, by attending any of the many available synogogues. they must not do these 4 things.
Then, by attnending the synogogue. they will learn the Law of Moses over time. They were learn all the rest of the laws such as do not steal, murder, lie, etc. and the others. During this time, they are under grace, withou the same obligation as a Jewish person who was raised under these laws. But that grace is not an excuse to sin. as the bible teaches:
[Rom 6:1-2 KJV] 1 What shall we say then? Shall we continue in sin, that grace may abound? 2 God forbid. How shall we, that are dead to sin, live any longer therein?
Therefore there is grace for the gentile, not that they have to keep the law, but that they get to! (Even though they do not have the same obligation as a Jewish person). So why would they do this? Because they love the lord and want to keep his commandments. There's spiritual rewards that come from doing so as well. Now no one is saved by keeping the Law, only what Jesus did on the cross saves us. But beyond the question of salvation there is a reward for it, for the bible says:
[Mat 16:27 KJV] 27 For the Son of man shall come in the glory of his Father with his angels; and then he shall reward every man according to his works.
The reward however is not the motivation. The true motivation is our love for Jesus, because he said that we can express our love toward him by keeping his commandments.
The bible also says that those gentile who become Christians are "Circumcised in the heart" and therefore are accepted by God and may freely follow him without being required to also become physically circumcised in the flesh to be saved.
[Col 2:10-12 KJV] 10 And ye are complete in him, which is the head of all principality and power: 11 In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: 12 Buried with him in baptism, wherein also ye are risen with [him] through the faith of the operation of God, who hath raised him from the dead.
[Rom 2:29 KJV] 29 But he [is] a Jew, which is one inwardly; and circumcision [is that] of the heart, in the spirit, [and] not in the letter; whose praise [is] not of men, but of God.
For more on this topic, I recommend getting the book entitled "The Heart of the Kingdom: God, Israel and the Church" by Tomas N. Deplume, by clicking here.