All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
When a person is merely convinced about the religion of Islam and acknowledges it, this is not enough for him to be a Muslim and he is not called a Muslim. Abu Taalib, the uncle of the Prophet, sallallaahu ‘alayhi wa sallam, admitted the truthfulness of the message of Islam as well as the trustworthiness of the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, but he did not prove this through his words and deeds and remained a non-Muslim. We seek refuge in Allaah from this.
If a person embraces the religion of Islam, the Islamic rulings are applied to him and he becomes a Muslim entitled to the same rights and liable to the same duties as any other Muslim and he is permitted to marry Muslim women. But, if he remains Christian --despite his claim that he is convinced about Islam, he is still a non-Muslim. In this case, it is impermissible for a Muslim woman to marry him whatever the case may be. Allaah The Almighty Says (what means): {And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you.} [Quran 2: 221]
Allaah Knows best.