How Are Children Sanctified In 1st Corinthians 7:14

I often use BibleHub.com, which is a helpful resource. Pastor John Ellicott (1819-1905) says this about 1st Corinthians 7:14 in his Bible commentary:

The children of such ​[Christian] marriages were considered to be Christian children; and the fruit being holy, so must we regard as holy the tree from which it springs.​ ​It must be remembered that the "sanctification" and "holiness" here spoken of is not that inward sanctification which springs from the action of the Holy Spirit in the individual heart, but that consecration which arises from being in the body of Christ, which is the Christian Church (Romans 9:16.)​ SOURCE

In his The Strand Study Bible, on page 1885, Pastor Brad Strand comments concerning 1st Corinthians 7:14:

“​God's view of a home changes whenever there is a Christian within the household. Because of the presence of a believer within the home, God sanctifies that home in a positional sense. That is, the couple will share in God's blessings because of the saved spouse.” —Pastor Brad Strand, 'The Strand Study Bible,' p. 1885; Rood Scholar Press, © 2009

I found a free online .pdf version of The Strand Study Bible. I recommend that you download it to save. It's about 170 MB in file size. This commentary sells as a hard copy on Amazon.com for $138.