That was the question, and Paul devotes all of chapter 7 to it.  In view of the impending return of Christ and the culmination of history, it is better not to get married (1 Cor 7:29).  On the other hand, it is better to marry than "to burn with passion" (1 Cor 7:9).  Paul shared with the leaders of the Jerusalem church the belief that world history was at a crisis point (1 Cor 7:26).  Believers should be singlemindedly devoted to Christ, and not distracted by family ties.  

           

None of this has anything to do with race, except the following verse:

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           A woman is bound to her husband as long as he lives.  But if her husband dies, she is free to marry anyone she wishes, but he must belong to the Lord (1 Cor 7:39).

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There is a lot in this verse, both said and unsaid:

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           -- "anyone she wishes"?  Wow!  No racial limitations.  He could have said: "Jewish believers must marry circumcised men, Gentiles must marry uncircumcised."  That would have been a good way to acknowledge the continuing authority of traditional morals.  By not saying this, he tacitly abolished Jewish marriage laws.  This also overturns and annuls the basis for 19th Century American miscegenation laws.

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          -- "but he must belong to the Lord."  This is the replacement ethic for racial segregation.  It is the only limitation on her choice of a spouse, but it is just as powerful as the previous exclusion.  A widow of Jewish background could marry a Gentile believer, but she was prohibited from marrying a non-believing Jew whose family she had known all her life.  This was a major line of demarcation between the new faith community and non-Christians.  It is still a point of contention today among the various Christian denominations.

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          -- "she is free."  Wait a minute, this is Paul.  Modern hermeneutics has asserted that Paul is the source of New Testament patriarchy, by forcing women to be silent in churches and wrapping them in obligatory head-coverings.  But in this passage, Paul says the widow has the right to marry or not whomever she wants.  Logically, we might extend this authority to the widower as well.  But the point is -- Paul's focus was explicitly giving the woman a power of decision.  Only implicitly do we extend that power to men.

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          --  another extension of this verse is to apply it not only to widows, but to non-widows.  All believers are under the same freedom and obligation: freedom to marry whomever, so long as he/she is a believer.

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          --  there are other protections for women in this chapter that the feminists ignore.  A believing husband cannot divorce a non-believing wife who wishes to stay married.  Nor can a believing wife force her non-believing husband to divorce.  In such cases of mixed cohabitation, the unbelieving spouse is counted as "sanctified" through the believing spouse.  But if the unbeliever insists on leaving, then they may divorce.

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           Paul's point in this chapter, as in the entire book, is to maintain and promote unity and righteousness within the infant community.  Pre-existing family relationships are recognized as valid in God's sight.  The New Covenant brings with it a new freedom in forming marriages, so long as that Covenant is honored by both parties.