Sin is a separation from God - it does not mean that the person is evil, or has actually has horrible thoughts/words/deeds. From this angle, a baby is sinful because he does not have a relationship with God.
Baptism is a public acknowledgement of a real relationship with God so it clears the original sin inherited from Adam.
As an Anglican, I have not come anyone bringing their babies for baptism who do it to wash away original sin. They do it to welcome their baby in to the family of God.
Of course, we all keep sinning after baptism because we still have an earthly nature, but through confession, prayer, etc, we can keep righting our relationship with God.