I will endeavor to answer this question as it would have been understood by people at the time.
Although the 2 Corinthians passage may or may not have immediately brought marriage to mind, another passage certainly would have. Speaking of the other civilizations in the region, the Lord said in Deuteronomy 7:
3 Neither shalt thou make marriages with them; thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son.
4 For they will turn away thy son from following me, that they may serve other gods: so will the anger of the Lord be kindled against you, and destroy thee suddenly.
So there was certainly precedent for seeking to marry within the faith lest one be led away from God.
Overlap in religions
However, it is worth noting that at the time 2 Corinthians was written (AD 55 or 56), Judaism & Christianity were still widely considered to be the same religion. Three examples of this:
And a certain Jew named Apollos, born at Alexandria, an eloquent man, and mighty in the scriptures, came to Ephesus…For he mightily convinced the Jews, and that publickly, shewing by the scriptures that Jesus was Christ. (Acts 18:24,28)
Apollos is clearly considered a Jew who believes Jesus is the Messiah—his preaching is not to convince Jews to change religion, but to show that Jesus is the fulfilment of the prophecies of the religion they already believe.
From Paul himself, within a year or so of writing 2 Corinthians:
For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek. (Romans 1:16)
This suggests a pretty inclusive view of the faith at that time.
And from the point of view of Rome:
1 After these things Paul departed from Athens, and came to Corinth;
2 And found a certain Jew named Aquila, born in Pontus, lately come from Italy, with his wife Priscilla; (because that Claudius had commanded all Jews to depart from Rome:) and came unto them. (Acts 18:1-2)
We also know from Dio Cassius that Claudius commanded the Jews to depart from Rome (although enforcement was rather lax, see Roman History 60.6.6-7), and Acts explicitly says that Aquila was a Jew and the Jews were commanded to leave—but we learn from Acts & Paul that Aquila & Priscilla were decidedly Christian.
So we’re talking about a time when Christianity was seen as a subset of Judaism, which continued until the Flavian era (70s-90s see here).
Conclusion
I believe the passage leaves the OP’s question open to interpretation by people at the time. They believed they should marry within the faith, but in the first few decades after Easter “the faith” was still Jewish.
So a baptized Jew might see nothing wrong with marrying a non-baptized Jew, seeing themselves as members of the same faith; or a baptized Jew might determine that the spirit of the law from Deut. 7 indicates that marriage to a Jew who does not believe in Christ would be a source of spiritual friction.
Paul may well have intended this as counsel regarding marriage between those who did vs. did not believe in Christ, but he was not so forceful in his delivery that people of the time couldn't interpret it different ways.
Post-script from modern parallels
Two related question…showing the variety of possible interpretations… would be these:
Would members of different sects of Judaism intermarry? Sometimes yes, sometimes no
Do Christians of different denominations believe it is appropriate to marry a Christian of another denomination? Interpretations vary widely in the present day.
Many denominations within the same family of religion see other denominations to be in grievous error, and therefore their counsel not to marry outside the faith is denomination specific—they are concerned for people’s eternal welfare if they marry into a denomination whose teachings are held to be heretical.
I suggest the varied interpretations seen today are not all that different from the way baptized Jews would understand Paul’s meaning circa AD 56. Paul is writing for the Corinthians in the 50s, at a time when the problem was less acute than it would become several decades later.
