“Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill” (Matthew 5:17). This statement from Jesus is key to understanding the relationship between the old and the new covenants. Everything associated with the old covenant is being fulfilled in the new, not abrogated. This variety of supersessionism is not primarily a matter of punitive replacement, but of fulfilling what God had intended from the beginning. There is thus no discrediting of the old, for it has successfully accomplished its limited purpose. Furthermore, its promises are still in effect, but are properly understood as applying to the remnant that accepts and follows the Messiah.
So it is the church, the body of Christ, who are the heirs of the promises and the descendants of Abraham. But the church has continuity with – and is rooted in – the Israel of the old covenant. There is one olive tree, rooted in the Jewish Messiah, which now has Gentile as well as Jewish branches. The Jews were chosen for a special mission, but their means of salvation is precisely the same as for the Gentiles: i.e. in and through the Jewish Messiah. God shows no partiality, nor should we.
If the above is a kind of “supersessionism”, then the gospel of NT scripture is supersessionist. But I think it is more precise to speak of fulfillment, wherein Jesus Christ is the only way, and in which there is no longer any distinction or partiality. To consider Jews according to the flesh as entitled to anything less, or anything more, would be clearly contrary to scripture, and would deny the fulfillment revealed in scripture.
The NT makes it clear that Jesus Christ is a stone that many will stumble over. The gospel of the cross is offensive and scandalous – understandably more so for Jews than for Gentiles. But we must not compromise this gospel to soften the scandal or to avoid offensiveness. We must not allow theology to be driven by feelings of sympathy or guilt over Jewish persecutions. We must not propose an alternative gospel for the Jews, supposing it to be an act of kindness. False words of comfort are not kind. We are rather to speak the truth, in love, just as Paul did in Romans 2-4, 9-11. It is by this that we can be true friends to the Jews. One might label the gospel as “supersessionism”, but it is not anti-Semitic.