The phrase “throughout your generations” in Gen 17:9-14, means not just this generation, but generations to come. The generations referred to in Gen 17:9, are the Jewish people. In the context of the covenant of circumcision “throughout their generations” is ended by the coming of the promised Messiah, ie Jesus. The circumcision that both Jewish and gentile believers now require, is to put off the flesh. In other words, we must die to serving sin and live to God.
Rom 6:11-13 So you also must consider yourselves dead to sin and alive to God in Christ Jesus. (12) Let not sin therefore reign in your mortal body, to make you obey its passions. (13) Do not present your members to sin as instruments for unrighteousness, but present yourselves to God as those who have been brought from death to life, and your members to God as instruments for righteousness.
So circumcision is now of the heart, or symbolic, not literal. Paul explains this in Colossians 2:
Col 2:11-14 In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ, (12) having been buried with him in baptism, in which you were also raised with him through faith in the powerful working of God, who raised him from the dead. (13) And you, who were dead in your trespasses and the uncircumcision of your flesh, God made alive together with him, having forgiven us all our trespasses, (14) by canceling the record of debt that stood against us with its legal demands. This he set aside, nailing it to the cross.
This is a much more meaningful thing than physical circumcision. In Galatians 5, Paul emphasises the fact that physical circumcision is no longer required:
Gal 5:2-6 Look: I, Paul, say to you that if you accept circumcision, Christ will be of no advantage to you. (3) I testify again to every man who accepts circumcision that he is obligated to keep the whole law. (4) You are severed from Christ, you who would be justified by the law; you have fallen away from grace. (5) For through the Spirit, by faith, we ourselves eagerly wait for the hope of righteousness. (6) For in Christ Jesus neither circumcision nor uncircumcision counts for anything, but only faith working through love.
So Jewish people today who are not literally circumcised will not be “cut off from his people”. However, if they do not accept salvation on God’s terms, through Jesus Christ, they will eventually be cut off.
Unfortunately, James and the elders say otherwise in Acts; physical circumcision is not ended by the coming of Jesus Christ. Consider first that Paul had Timothy physically circumcised according to Acts 16:3. Secondly, consider the words of James and the elders to Paul in Acts 21, and Paul’s response and subsequent actions:
“When we had come to Jerusalem, the brothers received us gladly. On the following day Paul went in with us to James, and all the elders were present. After greeting them, he related one by one the things that God had done among the Gentiles through his ministry. And when they heard it, they glorified God. And they said to him, “You see, brother, how many thousands there are among the Jews of those who have believed. They are all zealous for the law, and they have been told about you that you teach all the Jews who are among the Gentiles to forsake Moses, telling them not to circumcise their children or walk according to our customs. What then is to be done? They will certainly hear that you have come. Do therefore what we tell you. We have four men who are under a vow; take these men and purify yourself along with them and pay their expenses, so that they may shave their heads. THUS ALL WILL KNOW THAT THERE IS NOTHING TO WHAT THEY HAVE BEEN TOLD ABOUT YOU, BUT THAT YOU YOURSELF ALSO LIVE IN OBSERVANCE OF THE LAW. … Then Paul took the men, and the next day(AL) he purified himself along with them and went into the temple, giving notice when the days of purification would be fulfilled AND THE OFFERING PRESENTED FOR EACH ONE OF THEM.
– Acts 21:17-24,26, ESV
You have misunderstood Paul as Peter warns in 2 Peter 3. Paul teaches that the believers from all the nations are saved by faith in Christ Jesus, not by ritual conversion to Judaism, which, in the vernacular of Judaism, is referred to as “circumcision.” It is said, all Jews have a part in the World to Come, so you just need to become a Jew to be saved. If that were true, then Messiah died for nothing. No, God shows no partiality, as Peter says, but IN EVERY NATION, EVERYONE WHO FEARS GOD AND DOES WHAT IS RIGHT IS ACCEPTED BY HIM.
Be careful not to be led away with the error of lawless people, as Peter warns. As Christ Jesus says, do not think that I have come to destroy the Law or the Prophets. Whoever breaks one of the least of these commandments and teaches others to break them will be called least in the kingdom of heaven, but whoever does them and teaches them will be great.
It is true that Paul had Timothy circumcised. However, the “Why?” does not seem to be because all Jews everywhere were required to be circumcised, but “because of the Jews who were in those places”. Presumably he knew it would affect the ministry to the Jews at that time if Timothy were not circumcised. That doesn’t say that all Jews must be circumcised.
Similarly, the fact that Paul still kept the law does not say anything about whether he required other Jews to still keep the law. The passage in Acts 21 does not address it at all: James is merely trying to keep Paul safe and out of trouble (a thing that ultimately proved impossible).