Denominational teaching on baptism is contradictory

Baptism is not a requirement of salvation, but it is a requirement of obedience.

If obedience is necessary for eternal salvation, as it most certainly is according to Hebrews 5:9, since Jesus "became the source of eternal salvation to all who obey him," then how can baptism be a requirement of obedience but not of salvation? This denominational doctrine is a clear and direct contradiction of all New Testament teaching, both on baptism and on obedience.