Who is the true inheritor to the promises of God in the Old Testament the Church or the synagogue?
***All those of faith are inheritors of the promises of God. Before Christ, it was those Jews and others who came to have faith in God, the Father looking forward to and having faith in the coming of the Messiah (this would include Abraham and Moses, for example and the many other Jews and others of faith).
After Christ, it is those who have faith in, and accept, Jesus as Messiah, Lord and Saviour.***
Has the Church’ teaching regarding modern Judaism changed?
I don’t believe so - though there is a movement towards to the rediscovering and celebration of the Jewish roots of our faith.
Can Jews be justified without Christ?