As to them being drop cloths. Around my house when things aren't in good condition anymore, they get cut up and reused, either for mechanic's cleaning cloths, quilt squares or drop cloths when painting or when our dogs have puppies and the female needs a place that's kind of cozy--those will usually get tossed after use, though I may wash them (usually we use old towels).
Using a quilt for moving furniture really makes sense...if the quilt is old and in not very good shape. It wouldn't bother me to see an old quilt I made be used in this way. Now, the one I gave last year....it would bother me, but I'd try to get over it.