When Paul went up to Jerusalem, he had been teaching Gentiles that they are not converting to Judaism and they are therefore not under the Jewish covenant nor the Law associated with it. At the meeting in Jerusalem (Acts 15), Peter reports his experience with Gentile salvation and agrees that requiring Gentiles to keep the Law is placing an unnecessary yoke upon them (Acts 15:7-11).
When Peter describes the Law as a “yoke” on the Gentiles he is not necessarily criticizing the Law. In Judaism, the idea of being “yoked” to the Law is a positive image, although there is often the implication of completeness – if you are yoked to the Law, you are required to keep it all (Bock, Acts, 501). Here are a few examples of this view from Sirach (200 B.C.), the Psalms of Solomon (50 B.C.) and the Mishnah (A.D. 250, but perhaps reflecting an earlier oral tradition).
Sirach 51:26 Put your neck under her yoke, and let your souls receive instruction; it is to be found close by.
PsSol 7.8-9 For Thou wilt pity the seed of Israel for ever And Thou wilt not reject (them): But we (shall be) under Thy yoke for ever, And (under) the rod of Thy chastening.
PsSol 17:30 And he shall have the heathen nations to serve him under his yoke; And he shall glorify the Lord in a place to be seen of (?) all the earth.
m.Aboth 3:5 R. Nehunya b. Haqqaneh says, “From whoever accepts upon himself the yoke of Torah do they remove the yoke of the state and the yoke of hard labor. And upon whoever removes from himself the yoke of the Torah do they lay the yoke of the state and the yoke of hard labor.”
m.Ber 2.2 Said R. Joshua b. Qorha, “Why does [the passage of] Shema precede [that of] And it shall come to pass [if you keep my commandments]? So that one may first accept upon himself the yoke of the kingdom of heaven and afterwards may accept the yoke of the commandments.
Peter therefore seems to be saying that God saves both Jew and Gentile by faith, but that God has only given the Law to Israel. The law is a yoke, but is is a yoke that the Jewish people accept. Peter agrees with Paul’s claim that Gentiles are not converts to Judaism, but rather Jews and Gentiles both are converts to something new, a new people of God, a new “body of Christ” (Eph 3:1-6). Peter is certainly not saying that Jews ought to disregard Law, but only that Gentiles ought not be given an additional burden that was given to the Jewish people.
I suspect that many (non-Jewish) Christians in the contemporary church would find the law to be a difficult burden, mostly because the western value of freedom. To a Jewish person in the first century, the Law was not difficult because it was exactly what God had called them to do. It was a responsibility, but also a response to the grace of God toward the Jewish people.
The Law was not something the Jewish people “had to do,” but rather something they “get to do” in order to honor their God.