STEP AWAY FROM THE MACHINE.
PUT THE QUILT DOWN.
Do not wash a quilt top before it's quilted.
It's not that it will all fall apart, but it will be a mess to iron again, as the seam allowances are all over the place, and frayed.
The fact that you think some fabrics might shrink at a different rate than others won't be solved. They'll shrink, but wouldn't be stabilized by anything.
Actually, you'll have more control over the shrinking if it's washed after it's quilted.