Here's the Logos commentary by R P Martin on 2 Cor 6:14 ff:
"If, however, a broader scope is given to ἄπιστοι here, we may ask what kind of union and to what extent Christians are to refrain from becoming yokefellows with non-Christians. On the one hand, it appears unlikely that Paul was asking the Corinthians to cease all contact with the Gentile world. He recognized that this was an impossibility (1 Cor 5:10), though his counsel was evidently misunderstood. In terms of business and ordinary social kindness, Paul would exhort the believers to be good witnesses (Filson, 352). Paul did not ask his converts to come out of the world (or even “to abstain from non-Christian dinner parties,” Barrett, 196). Also, we note how Paul became “all things to all men” (1 Cor 9:20–23).
"Rather, Paul warns against compromising the integrity of faith (Hughes, 246). Any action that would cause believers to link up with the world in thought or act (through indifference or connivance) must be avoided. Specifically, marriage (1 Cor 7:12–15) was one source of possible mismating."
That seems reasonable. Paul was writing to people whose major danger was probably falling back into pagan practices. Unfortunately Christians today are so split on the nature of the Christian life, that sometimes non-Christians may seem closer to living as Jesus taught than other Christians. I think that complicates any attempt to take this too literally.
