There is one theology and one attitude with which I will have no truck: Supersessionism and Antisemitism. I suspect that many need to ask themselves how much of each they may readily encounter in the congregations they frequent (no matter where they fall on any pre-conceived spectrum).
Although it is gratifying that our communion may have, on occasion, actually got something right, viz.
From the early days of the Church, many Christian interpreters saw the Church replacing Israel as God's people. The destruction of the Second Temple of Jerusalem was understood as a warrant for this claim. The Covenant of God with the people of Israel was seen only as a preparation for the coming of Jesus. As a consequence, the Covenant with Israel was considered to be abrogated.
This theological perspective has had fateful consequences. As Christians understood themselves to replace the Jews as God's people, they often denigrated the Judaism that survived as a fossilized religion of legalism. The Pharisees were thought to represent the height of that legalism; Jews and Jewish groups were portrayed as negative models; and the truth and beauty of Christianity were thought to be enhanced by setting up Judaism as false and ugly. Unfortunately, many of the early Church fathers defamed the Jewish people.
I consider that the founders had already set the correct temper and tone, several centuries ago: