Martin Luther offers useful commentary on 1 Cor 7:14, a difficult passage:
14. For the unbelieving husband is consecrated through his wife, and the unbelieving wife is consecrated through her husband. Otherwise your children would be unclean, but as it is, they are holy.
This is spoken in the Hebrew way and according to the manner of St. Paul, to the effect that all things are holy to him who is holy. Thus he says in Titus 1:15: “To the pure all things are pure”; or in Romans 8:28: “We know that in everything God works for good with those who love Him,” which is to say: A Christian spouse may not be divorced but can live with a non-Christian mate and even conceive and raise non-Christian children. The reason is this: if the non-Christian spouse does not prevent the Christian mate from leading a Christian life, then faith is such a mighty thing that no hurt will come from living with a non-Christian; it will make no difference whether he associates with religious or irreligious people, for even death, that most terrible thing of all, is still a holy thing for a Christian.
Faith can use all things for its purpose, whether good or bad, except unbelief and its fruits. For these are directly contrary to faith and do not permit faith to remain; those things that do permit faith to remain are themselves rendered harmless by faith, are made pure, holy, useful, and salutary, so that the believer may live with them and keep them without danger. If this were not so, no Christian could live, for he is forced to live among evil and non-Christian people. But if he does not follow them but puts them to good use, he may live with or among them to the end that they may gain piety and become Christians.
To a Christian, therefore, the entire world is holiness, purity, utility, and piety. Contrariwise, to a non-Christian the whole world is unholiness, impurity, uselessness, and destruction—even God with all His goodness, as Ps. 18:26–27 says to God: “With the pure Thou dost show Thyself pure; and with the crooked Thou dost show Thyself perverse.” Why is this? Because the pure, that is, the believers, can use all things in a holy and blessed way to sanctify and purify themselves. But the unholy and the unbelievers sin, profane, and pollute themselves incessantly in all things. For they cannot use anything in a right, godly, and blessed way, so that it might serve their own salvation.
In the same way children are also holy, even though they are neither baptized nor Christians. They are not holy in themselves (St. Paul is not discussing this holiness here) but are holy to you, so that your own holiness may associate with them and raise them without profaning you, just as though they were holy things. St. Paul also wants to convey this: If a Christian spouse should have grown children with a non-Christian mate (as often happened in those days) and the children should not want to be baptized or become Christians, then, inasmuch as no one should be forced to believe but only willingly be drawn by God through His Gospel, the father and mother should not abandon the children or withdraw or fail in their motherly or fatherly duties, as though they could thereby sin and pollute themselves in unbelieving children; rather they should guide and care bodily for these children as though they were the holiest of Christians. For they are not impure or unholy, Paul says; that is, your faith can demonstrate itself in them and thus remain pure and holy.
So it should be done now and at all times. Where children do not want to accept the Gospel, one should not therefore leave them or send them away but care for them and support them like the best of all Christians, commending their faith to God, so long as they are obedient and upright in all other things having to do with outward living. For parents can and should resist and punish outward evil acts and works. But nobody can resist and punish unbelief and an inwardly evil nature except God alone. Thus this text of St. Paul’s also concerns us and strengthens us, making all things holy and pure to the believer.
Luther, M. (1999, c1973). Vol. 28: Luther’s works, vol. 28 : 1 Corinthians 7, 1 Corinthians 15, Lectures on 1 Timothy (J. J. Pelikan, H. C. Oswald & H. T. Lehmann, Ed.). Luther’s Works (28:34). Saint Louis: Concordia Publishing House.