I'm always amused when people refer to "today's version" of Christianity, as if the core principles of Christianity were somehow altered during the days of the early church. Ask for some form of proof, you are given links to Arianism, a heresy. Ask for more, they point to the Council of Nicaea, as if this group of church leaders suddenly decided to change the core principles of Christianity in order to please Constantine or some such nonsense.
The reason you cannot be a Muslim and a Christian at the same time is because of Jesus Christ. No believing Christian can accept Christ and the teachings of Muhammed at the same time. It simply isn't possible. The core doctrine of Christianity has always been, and will always be, that Jesus Christ was and is God incarnate, and that His death and Resurrection paved the way to eternal salvation. Any belief that deviates from that core principle is not Christianity, was not Christianity, and never will be Christianity. Other than that, both faiths have alot to agree on.