I'm still trying to think of something that falls between "too icky to touch" and "not terrible enough to throw away".
That said, I've machine washed pieced tops on gentle cycle (air dried flat) with no problems at all and have also spot washed parts of others by hand. None of those were 'yuk' cases, they just needed some piecing markings washed away or needle holes closed up before sandwiching and quilting. There aren't any shrinkage variations with spot washing because my fabrics are prewashed.