This is an important topic that needs to be discussed on this page and this is something that is important and vital to the subject of the Christian message. We need to know as to who Christians are allowed to marry and who are of limits. Let's read 2 Corinthians 6:
"2 Corinthians 6:14 Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? 15 What harmony is there between Christ and Belial[b]? Or what does a believer have in common with an unbeliever? 16 What agreement is there between the temple of God and idols? For we are the temple of the living God. As God has said:
“I will live with them
and walk among them,
and I will be their God,
and they will be my people.”[c]
“Come out from them
and be separate,
says the Lord.
Touch no unclean thing,
and I will receive you.”[d]
“I will be a Father to you,
and you will be my sons and daughters,
says the Lord Almighty.”[e]"
This text makes it very clear that idol worship is certainly out of the question and can be extended to certain things in a given context, such as a problematic business venture that stems into immorality. We are to have jobs in the world but within moral and biblical parameters. The text can also be an exhortation not to marry unbelievers. For example, it is out of the question for Christians to marry Muslims, Atheists, Buddhists, Hindus and other groups. While Rabbinic Jews are not idol worshippers, because they deny the Gospel, marrying them is out of the question and I am not being disrespectful, I am being honest.
Christians are to marry Christians, mixed marriage between Christians and Non-Christians is not on even in the NT and this principle is carried over from the TANAKH, where the Jews were never allowed to marry idolaters.
Now what do we do about Christians who are married to unbelievers BEFORE they converted, let's read 1 Corinthians 7:
"1 Corinthians 7:12 To the rest I say this (I, not the Lord): If any brother has a wife who is not a believer and she is willing to live with him, he must not divorce her. 13 And if a woman has a husband who is not a believer and he is willing to live with her, she must not divorce him. 14 For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband. Otherwise your children would be unclean, but as it is, they are holy.
15 But if the unbeliever leaves, let it be so. The brother or the sister is not bound in such circumstances; God has called us to live in peace. 16 How do you know, wife, whether you will save your husband? Or, how do you know, husband, whether you will save your wife?"
In the context, if you have two people, both deniers of Christ when they married and one of them becomes a believer in Jesus, that isn't a problem, because they married BEFORE the conversion to place and not afterwards. What Paul lays down is some criteria in order for the family to get along and live in peace, with the hopes that the unbelieving person eventually becomes a believer in Jesus and the children become believers. While in this relationship, the believer needs to do all they can to lead someone to Christ by their words and deeds.
This however is NOT a justification for a believer who isn't married to marry an unbeliever, that is out of the question and this is reiterated in the New Covenant, thus applies to Christians
Hope this answers questions.