Here is my personal take on the situation. If the fabric is totally inappropriate for quilting, say sheer curtains or fabric so old it has dry rotted, I would set it aside to get rid of. Threadbare sheets, etc. I would designate for lining double knit quilts. I would NOT mix cotton with double knit but I would mix it with blends as I do that all the time anyway with no problems. Heavier fabrics like upholstery and drapery, could be used to line thinner cotton quilts or for a top or backing. I understand that your quilts go overseas, however, there are many homeless here in our country that sleep out all the time who would appreciate a sturdy, heavy warm quilt, especially during the winter months, but during the summer, too. The quilt would make the ground a little softer to lay on. The upholstery, double knit and other heavier quilts are great for the homeless and the "uglier" the better since they don't want someone to steal it because it is pretty; and darker is good since they probably won't see much washing. If your group didn't want to make quilts for this, it could be a side project that fabric could be donated for. I can't imagine a single cold homeless person saying, "OMG, I can't take this quilt. That is upholstery fabric and it just will NOT do." LOLOL
Anything too worn or faded to use on the outside can be used on the inside if it is big enough, or can be pieced together to make it bigger in the case of say, faded curtain panels. Since you are tying these quilts, the extra seams should not be an issue.
If it is too hard for someone to get the needle and tying material (yarn or whatever) thru the double knits, what about machine tacking? I think that is what it's called where you sew it together back and forth in just little spots scattered about?
Basically, I believe that there is a way to use MOST of what we have and that it should be used. I believe that people who are cold will not care what the item that warms them looks like. I know I would not. I believe there is a great difference in the kinds of donation quilts and what qualities they require. IE: If I am making a quilt for someone who is ill and undergoing chemo, I will make it beautiful and soothing and hopefully comforting. If I am making a quilt for an active duty military person, I will make it handsome, but rugged, comforting again and leave out the whites and pale colors. For a homeless person, as described earlier. But all of my quilts will have my love and caring in every stitch and will be done to the best of my ability. Some may be "ugly" in my personal opinion, but I know they will serve the purpose for which they are intended. And that is, after all, the whole point of making them.
I am proud to put my name on each quilt I made because they are made with love and caring and I have done my best. Not because they are a work of art that reflects well on my skill and talent as a quilter.
Sorry this turned into such a long post, but I feel deeply about this issue and it is so very important to me. Hugs and smiles and more hugs to each and every one of you who spend even a little bit of your time quilting to help others. All the differing opinions and discussions in the world cannot detract from the good that you do!!!