It’s not what goes into a man that defiles him, it is what comes out of a man that defiles him.
A person may be from a Muslim culture, be raised by his parents and nation to learn Islam, prays to God, but in his thinking if he places his relationship to God in His hands by His method of providing salvation, then that person might actually be a believer through faith in Christ. Even if he doesn’t know the letters of His name, the believer knows the meaning f the name in his heart when he believes.
Taking the Lord’s name in vain is more about taking the meaning of Him in vain, rather than the transliteration of his title.
It is possible for a person to pray to God the Father and not be heard, because the person seeking Him does so through arrogance and not by the protocols God has established for us to have fellowship with Him.
I concur though, with your point. The false prophet came along 600 years after our Lord was physically resurrected and ascended to heaven. The Koran is false doctrine. Accepting the Koran as a comparable access to God with cognizance of Christ is to deny Christ.
If his bothers some worldly folk, consider the prayers of Jesus Christ to God the Father in the Garden of Gethsemene, wherein He asked that if it was possible by any other means for him not to have to go through the ordeal he was about to experience. If one accepts Islam, then one must insist that the God of Jesus is not the same God as the god of Islam.