Use of the word circumcision by first century Jews didn’t mean only the physical surgery commanded in God’s instructions. It’s meaning had evolved to include much more. Tim Hegg M.Div., Th.M. and President of Torah Resource explains it this way in his commentary on Galatians (Paul’s Epistle to the Glatians, page 9).

“Here we must understand the term “circumcision” to be a short-hand way of referring to the ritual of the proselyte, the rabbinic ceremony in which a non-Jew was accorded the status of a Jew. So the question posed in Acts 15:1 is whether or not a non-Jew needed to gain the status of Jew through the rabbinic ritual of the proselyte in order to be counted as “saved”.

The Gospel of Nicodemus (an apocryphal document, dated between 150 to 400 CE) contains a chapter titled, Acts of Pilate. In this document, Annas and Caiaphas define a proselyte to Pilate as becoming a Jew.

“And Pilate, summoning the Jews, says to them: You know that my wife is a worshipper of God, and prefers to adhere to the Jewish religion along with you. … Annas and Caiaphas say to Pilate: All the multitude of us cry out that he [Jesus] was born of fornication, and are not believed; these [who disagree] are proselytes, and his disciples. And Pilate, calling Annas and Caiaphas, says to them: What are proselytes? They say to him: They are by birth children of the Greeks, and have now become Jews.” —  Roberts Translation

Josephus also describes circumcision as part of the process of becoming a Jew. (Antiquities of the Jews – Book XX, chapter 2, section 4)

“And when he perceived that his mother was highly pleased with the Jewish customs, he made haste to change, and to embrace them entirely. And as he supposed that he could not be thoroughly a Jew unless he were circumcised, he was ready to have it done. But when his mother understood what he was about, she endeavoured to hinder him from doing it; and said to him; that “This thing would bring him into danger; and that, as he was a King, he would thereby bring himself into great odium among his subjects: when they should understand that he was so fond of rites that were to them strange and foreign; and that they would never bear to be ruled over by a Jew.” (In case you are curious, the king ended up being circumcised anyway.)

For more background on proselytes, see this entry in the Jewish Encyclopedia.

Those who asserted circumcision (becoming a Jew) was necessary for salvation were adding to and misusing God’s law. It was a big enough problem that Paul’s letter to the Galatians is largely focussed on correcting this same false teaching. 

Modern readers don’t have much trouble agreeing that one does not need to become a Jewish proselyte to be saved. Yet many assume the only reason to obey God’s law would be for salvation. It is further asserted that since we can’t keep all of the law perfectly, then we should throw it out completely and rely on grace instead. However, this sets up a false dichotomy; “One must obey the law completely or not even try at all.” However, there are additional options.

First, law keeping is never presented in Scripture as being for salvation. Second, the Bible lists many other reasons to obey God’s law.

• One must obey to live among God’s people (Genesis 17:14, Exodus 31:14, Leviticus 17:10, Numbers 9:13, Deuteronomy 28:64) 
• Obedience is required for blessing and to avoid curses (all of Deuteronomy 28)
• Keeping God’s commandments is evidence of love for Jesus and the Father (John 14:15, John 14:21, John 14:23-24, 1 John 5:3, 2 John 1:6)
• Works of obedience to the law are an outward indicator of inner faith (James 2:14-26). 
• God’s law will remain the legal code of his Kingdom when our King lives among us again. (Zechariah 14:16-21, Jeremiah 33:18, Ezekiel 45:22)
• Obedience is evidence of God’s Spirit within, according to the New Covenant. (Ezekiel 11:19-20, Ezekiel 36:26-27)
• It is for freedom (Romans 8:2).
• It is for holiness and righteousness. (Romans 7:12, 2 Peter 2:21)

Should a man who wishes to be obedient to God’s law be circumcised (have the surgery)? There are benefits, as we just read, but circumcision (or becoming more Jewish) does not produce salvation.