"It never says that."
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Without faith it is impossible to please God. If the households remained unbelieving, then baptizing them only converted them from DRY sinners into WET sinners. The Ethiopian asked Philip the evangelist in the Book of Acts: "Here is a body of water. What prevents me from being baptized?" Philip answered: "If you believe in your heart, then you may".
The EXERCISE OF FAITH is the prerequisite to water baptism.
Show me where it says that every person in Lydia's "household" was a believer.
""It never says that."
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Acts 16:14-15--
14 And a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard [us]: whose heart the Lord opened, that she attended unto the things which were spoken of Paul.
15 And when she was baptized, and her household, she besought [us], saying, If ye have judged me to be faithful to the Lord, come into my house, and abide [there]. And she constrained us.