After reading all the posts, I can see that you are going with the navy squares.
I've put white in many of my baby quilts. Only had one occasion where the red ran into the white. That stopped after the first washing (with a color catcher).
One tip that I have for using white ----
BEFORE you sandwich with backing and batting, check the back of quilt for loose threads. They have a tendancy to show through the white. That also may happen if a colored seam is longer that the white seam when it HAD to be pressed to the abutting white piece.