We must be very sober when considering 1st Corinthians 7:24. The word "saved" is not used. "Sanctified" and "made holy" are used. That is, because of the STANDING of the ONE believing parent, the same STANDING is attributed to the rest of the family. Noah believed and God set in motion a means for him, not to avoid the Lake of Fire, but to avoid the flood - the universal judgement. His family was allowed to join him in the Ark. But we see later that one of the sons was far from good. But Ham, based on his FATHER'S standing was granted salvation, not from the Lake of Fire, but from the flood.
Again, we have the case of Lot. God told Abraham to leave his "kinsmen". Abraham was not 100% obedient and took Lot with him. Later he paid for this when they had a dispute about grazing rights. But Lot was RELATED to Abraham, so God approaches Abraham and reveals His plan for the Sodomites of the Jordan Valley. Abraham intercedes, and Lot, though far from perfect, is granted escape from Sodom. So is his wife and daughters. But we see from their actions afterwards that they themselves are far from holy. God grants mercy because of ASSOCIATION.
1st Cotinthians 7:24 does not grant automatic salvation and eternal life. But it might grant salvation from the Great Tribulation.