We are part of the Abrahamic tradition, whether you believe it or not does not change that for us. We are not saying that to please the Christians or the Jews. Except for some interfaith circles, the Jews and the Christians have always rejected us as being part of that continued tradition, as do many atheists, and others. However, it doesn’t put a dent in our belief that we are indeed the children of Abraham, spiritual and otherwise.
Abraham is no minor figure in the Quran. He’s the “Friend of God,” and very near and dear to Muslim hearts. I don’t really understand your dismissive attitude about what Abraham means to us. We believe Abraham was a “Muslim,” not a Jew, not a Christian, not a founder of a “new religion.” He was a Muslim like others before him were too, who believed in One God. He has more prominence because his progeny really spread across the Earth. A Muslim doesn’t encourage believers to convert to Judaism or Christianity because we believe that the Jews and then the Christians brought changes to God’s religion and altered the book, so reverting back to the “original” Abrahamic faith would be going backwards and accepting those changes that corrupted the Word of God.
I hope that explains that it’s not a PR stunt when we say that we indeed have a very real spiritual connection with Abrahim (may Allah bless him).