Your first sentence is right on. The second is off. Even God of the Bible says that if you don't worship Him as you are meant to, then you worship false Gods and you follow false messiahs (He says they will tell you they come in His name...like Mohammad). Becuase if you look at Mohammad and Jesus, there is no realistic comparison. One was a blood thirsty child molestor and the other refrained from sex his whole life and only became justifiably physically violent one time...as far as we know.
How do Jews fit into your analysis?