You've got my attention. I thought it was fundamental to all branches of Christianity.
I'm not too sure of the details, but I know none of the churchs I went to ever held to it. We tended to view it as a freaky Catholic thing. That was a Baptist church, but I don't know whether it was a general Baptist belief, or just the church I went to - but I assume that's one of the reasons they don't practice infant baptism. My mother's an ordained priest in the Church of England, and she doesn't believe it either. But the CoE's exceedingly broad in the range of beliefs it will accept, so again I don't know whether it is a core belief or not.
The view I was raised with was that no-one is without sin because humans are incapable of leading perfect lives, not because they are born that way.