Your are right. But I think our view is not popular. Most quote the law(though we are under grace) about the sins of the father visited upon the children to the 3rd and 4th gen. But under grace children under that age of accountability (about 13) are not responsible for there faith and thus are considered believers. God is not cruel he will not force a child to endure the wrath of the tribulation because of his parents wrong choice. I sometimes can't believe people think God love children of non-christians that little. His love for kids knows no religious barriers. He loves all mankind but after the age of accountability even though he loves you if you die not believing in him hell is all that awaits. Same for the rapture if you are above the AofA then if you are not christian or not doing Luke 21:36 then you are left behind. If you are christian above the AofA and doing Luke 21:36 or you are below the AofA then you will go.
 
Paul
 
"Lord, what fools these mortals be"