Paul had opinions. Strong opinions. He didn't mince words. Although (so far as we now) he was an unmarried man, he doesn't hesitate to give advice to married men and married women as well.
Personally I believe that no one on the outside can ever understand what goes on inside a marriage. What is seen in public may be utterly different and even opposed to what goes on in private. We married folk, for many different and good reasons, tend to put a good face on even when the interior is scowling.
So Paul is personally ignorant of the daily realities of marriage. But he does understand the difference between someone who knows eternal hope, and someone who denies it. He sees it (properly I believe) as an impediment in a marriage--but not grounds for divorce. Marriage is always worthy of respect and worth keeping intact. However--if your unbelieving partner leaves you, Paul advises that you not grovel to make them stay.
This is not a theoretical discussion for me. My wife believes in God and lives a life that is answerable to God. She loves unconditionally and sacrificially. But we have vastly different views of how that belief translates its impact to the wider community. When I said last week that I would not vote for an avowed atheist, she was shocked and disappointed that I could engage in "anti-atheist bigotry." She polled her friends and associates as well as her clergy, and the overwhelming consensus was against me. I may need to re-think my position; after all, a profession of faith has never been a guarantee of competence in elected office (or any other job). But I still have a fundamental discomfort with the prospect of being led by someone who denies what to me is a self-evident characteristic of the universe.
So we, like many couples, must agree to disagree, and (try, with mixed success, to) avoid being disagreeable in the process. It's not up to me to try to change her (nor vice versa). The marriage is imperfect but God blesses its imperfection. As I look back on nearly thirty years, it is abundantly clear that God is not done with either of us--nor with the two of us together.