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The quilts are all going overseas. We're not actually quilting them, just tying through with perle cotton (or similar). I don't believe all the fabrics would wash succesfully, but the point was mentioned that if the quilts are just to serve as a wall or a rug, they might not ever get washed anyway........................
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I'd take any fabric that isn't strong enough for washing and get rid of it somehow, at least separate it from the washable------------Personally, I'd be very upset if I got a quilt thinking I could wash it when soiled and then find our the thing fell apart.
When our group did charity quilts, we had some knits and such. We always paired the knit with a good woven and ended up with some cute quilts.