They don’t just claim to worship the same God, but do! All Christians believe in the creeds of the church written by the church fathers, such as the Apostles’ Creed, the Nicene Creed, Athanasian Creed, and the Chalcedonian Creed. What makes a sect or faith Christian is whether they believe in the Trinity: God the Father, God the Son, and God the Holy Spirit, all coequal, coeternal, and co-existent. It is the sects that deny equal status to Jesus as God the Father and make Him less than full deity.
There are only minor differences of opinion (people are human and can interpret certain passages of the Bible in a different light) and on areas that are only minor such as mode of baptism, church government, mode of communion, types of worship. Most Protestants feel they can get along with all other Protestants because they all oppose Roman authority over the church and its members; however, most believe Catholics are believers with irreconcilable differences. Most however Christians would concur with St. Augustine: “In essentials, unity, in nonessentials, liberty; in all things, charity.” Amen!