Why do we assume 2 Corinthians 6:14 has anything to do with marriage, or marriage specifically? There's nothing in the immediate context to even suggest it. Nowhere before or after the whole passage, or even within the passage, is Paul discussing marriage or any kind of relationship. So why do we apply this to marriages specifically?
My point is that nothing in any of the verses preceding 14 has anything to do with marriage or relationships. It's a weird, jarring transition to suddenly go from explaining or defending your apostleship to "don't marry unbelievers." And the language itself doesn't really necessitate that interpretation either. There's no actual mention of marriage itself in 14. Another thing too that's weird in the verse. There's no word in the Greek for "with" in this sentence. The translation we usually have is really from the Latin, "nolite iugum ducere cum infidelibus", which literally reads, "Don't lead the yoke with unbelievers." But the Greek literally says, "Don't become differently yoked by/to/for untrusted/unbelieving [people]." You'd expect the preposition "sun (syn)" meaning "together with" but it's not there. I checked the Textus Receptus, Byzantine, and Critical Texts and it's not present in any of them. It's just the plural substantive in the dative case. That's actually weird. There are three different prepositions which could have been used for "with" but none of them are present. Now, There are also about four hundred years in between the Greek of Paul's writing and the Greek which Jerome would have known when he translated it in the fifth century. That's almost to the point of unintelligibility between different stages of the same language. I kind of wonder if language evolution had anything to do with how he rendered it.
Regardless, interpreting it as meaning "don't marry unbelievers" doesn't fit the preceding context or anything afterwards. It also somewhat contradicts what he said in 1 Corinthians about not leaving an unbelieving spouse if they're content to stay married to you. If Paul had applied the same reasoning that he does in the rest of the chapter, he would have encouraged them to leave. Something doesn't mesh.
It makes more sense in the context of both of Paul's letters to Corinth that Paul is talking about not being "unequally yoked" with, as he says in 1 Corinthians 5, "anyone named a brother who is immoral, greedy, a slanderer, drunkard," and so on and "not even to eat with such a person. In truth, in his letters to the Corinthians, this is the only group of people that he is so harsh with, those who call themselves Christians but "whose god is their belly, whose glory is their shame, who set their minds on earthly things." This makes perfect sense when he says "don't be unequally yoked by the untrusted/untrustworthy/unfaithful. As he writes of those outside of the Church, "I didn't tell you to keep away from those on the outside of the Church, otherwise you'd have to leave the world completely, but to not keep company with the one named a brother who is immoral..." This interpretation also fits the harsh language he uses in the rest of 6 where he quotes from the LXX, "Exit out from the middle of them and be excommunicate [from them] says the Lord." As I wrote before, Paul did not have marriage or other personal relationships with "those on the outside" in mind when he wrote these words, but continued communion with those named Christians who do not actually live as Jesus Christ taught or walk as He walked. This should also be illustrated in that, in 1 Corinthians 7, believing spouses were not to divorce their unbelieving spouses if they consented to live with and remain married to them.
Paul wasn't forbidding interfaith marriages, he was reiterating a point that he makes over and over again, that the Corinthian Christians should have nothing to do with and no communion with those who, as John describes, claim to walk in the light but walk in darkness instead.

 
 
