I agree, I would make the quilt and then wash it either with color catchers (several) or Retayne. One time I put a just-finished blue and white quilt in the washing machine. The water turned blue so I immediately took the quilt out and let it air dry. I bought a box of Shout color catchers at Walmart and washed the quilt with two color catchers - it was a small quilt - the white stayed white.
I usually pre-wash my fabrics but I have a friend who never does. She washes the finished quilt with Retayne and has had no problem with colors running.
Judy