Despite the differences that exist between them in the Middle East, Jews and Muslims share a common heritage. Both trace their traditional lineage back to Abraham, the Jews through Isaac and his son Jacob; the Muslims through Ishmael, Abraham's son through Sarah's handmaid, Hagar. As a result, the ancient texts are sacred to both. As the group name implies, Islamic people consider Jews and Christians to be "People of the Book" because of their common heritage and their belief in the same God.
Also, both were attacked by Christian forces, particularly in Spain during the Reconquista. By protecting the Haggadah, they were in essence protecting a substantial portion of their own heritage shared with the Jews. Since the Sarajevo Haggadah is one of the oldest Sephardic texts still extant, it has special meaning to Islamic people and Jews.