There is nothing false about Islam being a religion.Islam is just as much as a religion as Christianity,Mormonism, Catholicism, Judaism and so on.
Religion | Define Religion at Dictionary.com
1.
a set of beliefs concerning the cause, nature, and purpose of the universe, especially when considered as the creation of a superhuman agency or agencies, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs.
2.
a specific fundamental set of beliefs and practices generally agreed upon by a number of persons or sects:
the Christian religion; the Buddhist religion.
3.
the body of persons adhering to a particular set of beliefs and practices: