False. This is not true from a Muslim perspective.

From Quran 2:62

“Surely, those who believed in Allah, and those who are Jews, and Christians, and Sabians, -whosoever believes in Allah and in the Last Day, and does good deeds - all such people will have their reward with their Lord, and there will be no reason for them to fear, nor shall they grieve.”

Belief in the One God is what's important. Whether you call yourself a Muslim, Christian, Jewish or other - e.g. Sabians.