Not all without exception but all without disctinction

The idea is that Christ death was a death that went out towards different kinds of people not just towards certain kinds. As was the case for the old dispensation where God chose a people for Himself to further out His redemptive purposes. Jesus was born of the Jewish religion not of the Greek system where the belief was pagan. Jesus was a Jew. Salvation was from the jews scripture says. To the Jew first then to the Greek. The Jews were God's chosen people in that the Messiah came from them (Romans 9:1-5). Of course this does not mean that under the old testament dispensation that there were no pagans who were brought from Darkness to Light. However, they had to become Jewish. An offshoot of this is that the Christians in Acts were wondering whether to make Gentile Christians to first become Jews so that they could become Christians. But the conclusion made was no for salvation is by Grace Alone which is the point of the letter to the Galatians.
Of course the wall of seclusion was not knocked down until after Jesus accomplished his mission. The seclusion was that only the Jews were God's people and anyone outside of Jewish community were considered filthy.
The statement made in John 3:16 was astounding for the purpose - John writes was to show that God qualitative love was not just toward the Jewish audience but extended out toward the rest of the world of the gentile. So when scripture makes reference that Christ died for all people it should really be read as all kinds of people. The atonement was in fact particular in intent in that God purposed that Christ should die for the salvation of His elect those whom He had Chose since before the foundation of the world who were spread abroad throughout the world.
The good news is that now the gospel is for all kinds of people. it is not just for the wealthy or the poor people but all people are to repent of sin and trust in Christ for righteousness sake. 1 Timothy 2 speaks of this truth. So today where one might be born in a Christian home the temptation might be that because He is of the Christian family he is saved. This is not true at all. Scripture says for all have sin and fall short of the glory of God. Therefore all must find there refuge in Adam number two. The idea is that as we preach the gospel to all people only those whom the Father has chosen to come to faith in His Son Jesus Christ will come by the regenerating work of the Holy Spirit who works so graciously and free (Ephesian 3:14-19).
Now this by no means says that Christ died for all men without exception that all men everywhere universally have been bought with a price by the blood of Christ for certianly He died for only His elect people whom God chose most freely in eternity past. Only God's elect will come to faith at the hearing of the gospel at the particular point that God decreed. The reprobate will be hardened by God's good providence.

A good book to read on this subject is Abraham Kuyper's Particular Grace