"This is the common party line, the story that all churches teach" is not a valid anything, certainly not an argument.
But this "party line" is directly from the Scripture. Eph 2:1-10 for example; or Romans 3:9-18; or 1 Cor 15:22; or Romans 5:6-19. If you do not believe that those scriptures teach that all are born as sinners, then just to say they do not is not adequate. We all are full of opinions. For the sake of preaching truth, you would need to show how the "common party line" has gotten it wrong. Line by line, precept upon precept.
All humans, including children of the devil, are born into a physical flesh body that is fallen. For that reason, it is part of the curse of original sin. Our flesh is sinful from the start, yes. Jesus' flesh was susceptible to sin as well, but He never once sinned.
Regardless of this, there is still a fundamental difference between the children of the wicked one and a child of God.
Consider the 'of the world'/'not of the world' concept.
Jesus tells His people that we are in this world, but not
of it. Jn. 17:14, 16
He says the opposite about the children of the devil.
"Ye are of God, little children, and have
overcome them: because greater is He that is in you, than he that is in
the world (the people of the world/the children of the devil).
They are of the world: therefore speak they of the world, and
the world (the people of the world/the children of the devil) heareth them."
1 Jn. 4:4-5
Jesus even specifically states that He is from above and
they are from below. He is from heaven and
they are from this fallen world.
He generated Adam and Eve and
their father the devil generated the Tares.
Jn. 8:23, 43-47
Matt. 13:38-39