What's the Biblical position on interfaith marriage? Here are some classic prooftexts on the subject:
3 You shall not intermarry with them, giving your daughters to their sons or taking their daughters for your sons, 4 for they would turn away your sons from following me, to serve other gods. Then the anger of the Lord would be kindled against you, and he would destroy you quickly (Deut 7:3)
For when Solomon was old his wives turned away his heart after other gods, and his heart was not wholly true to the LORD his God, as was the heart of David his father (1 Kgs 11:4).
A wife is bound to her husband as long as he lives. But if her husband dies, she is free to be married to whom she wishes, only in the Lord (1 Cor 7:39).
Do not be unequally yoked with unbelievers (2 Cor 6:14).
The danger of interfaith marriage is twofold: (i) Divided loyalties between a Christian's devotion to God and his devotion his spouse, and (ii) sending mixed signals to their kids.
To some degree, Deut 7:3 might reflect defunct Mosaic purity codes. The need to separate what is ritually pure from what is ritually impure. But even if that is timebound, the prohibition includes a timeless psychological principle. And the cautionary tale of Solomon illustrates that psychological principle.
It isn't clear that 2 Cor 6:14 has specific reference to marriage. In context, it could be referring to participation in the public and private idolatrous religiosity of pagan Corinthians. And that would be a challenge for Christians. However, in one or two ways it might still be germane to the question of interfaith marriage:
i) It might reflect a general principle about forbidden attachments or emotional entanglements.
ii) Interfaith marriage might be analogous to participation in pagan rites.
But even assuming that 2 Cor 6:14 either refers to interfaith marriage, or is applicable to interfaith marriage, who are the "unbelievers"? In the context of Roman Corinth, they'd be practicing pagans.
The "in the Lord" phrase in 1 Cor 7:39 is a bit ambiguous. But in the context of Roman Corinth, that probably stands in contrast to a pagan spouse.
How does that correspond to the situation of contemporary Christians. In some cases, the correspondence is direct. Paganism is not a dead religion. Take folk Hindus and folk Buddhists. You also have "Wiccans".
So, in general, 1 Cor 7:39 and 2 Cor 6:14 prohibit marriage between a Christian and a pagan. That's fairly clearcut, although many Hindus and Buddhists are merely cultural Hindus and Buddhists. Nominal pagans (as it were).
Besides direct comparisons, analogous cases include marriage between a Christian and a Muslim or a Christian and an atheist. Even though those aren't pagan, they are hostile to the Christian faith. I mean the religion or ideology, not necessarily the individual. But that can be dicey to untangle.
Then you have the question of marriage between a Christian and a Jew. That's a borderline case. Paul's strictures don't directly address that issue. It's clearly not equivalent to paganism. But is it analogous to paganism? That has to be heavily qualified. Traditional Judaism is antithetical to paganism. But many Jews are hostile to Christianity. Yet Paul himself was both Jewish and Christian. In principle, these are complementary rather than contradictory.
Of course, modern Judaism ranges all along a broad political, ethical, and theological spectrum. So that's further consideration.
Another complication is that in Paul's discussion, there are actually two opposing dangers. On the one hand there's the danger of getting married to someone who's morally and religiously unsuitable. On the other hand, there's the danger of remaining single, for that raises the risk of succumbing to sexual temptation–especially for younger men and women. So the danger isn't one-sided. Interfaith marriage is hazardous, but celibacy is hazardous.
Indeed, one reason Paul discusses the issue of single Christians is because the available pool of eligible Christians would be so shallow in the overwhelmingly heathen culture of mid-1C Corinth. So that creates a dilemma. He himself admits that celibacy is inadvisable in most cases.
Although there are many situations in which interfaith marriage is prohibited or imprudent (see above), it isn't always that straightforward inasmuch as there are situations in which we need to balance two competing principles. That's when borderline cases may come into play.