We want our feet to fall towards parallel when we walk but it is of the utmost importance they find their way there from a rotation of the pelvis not from turning the feet in. The feet will fall naturally towards parallel if the thighs move underneath the pelvis. The pelvic shift that brings the legs under the spine allows you use the whole foot and move forward from your core.
It is highly unlikely that you are using your core if you are falling to the outside of the feet.