How about this?
In 1 John 3:9, the context is that "sin is the transgression of the law" (1 John 3:4) so John may not have been referring to what Peter spoke of in his epistle when he spoke of sin?
I will say that I believe that when the Gentile believers that we read about in Acts 15 were converted, that God "purified their hearts by faith".
If Peter gave practical teaching on what it means to be born again in his epistle, I don't think that he was saying that those who are born again generally bear the attributes of sin that he spoke of in those verses.