This is a common problem. There can be other issues, such as items which are badly constructed or need repairs. These things all take time to resolve, and for me, they take a toll on my psychological well-being. My project right now is to inspect and "fix" several dozen double fleece tied fringe blankets donated for children. None have square knots, none have the layers stitched together at any point, most have not trimmed the selvages off, and a few have pet hair on them.
I think that each group leader needs to make a decision as to what is worth spending the time on and what isn't. Although most quilts, blankets, fabric, etc. are donated with wonderful intentions, keep in mind that some things are given in the hopes that "someone can do something with this." If they hadn't found your group to give it to, they would probably have discarded the item, since they didn't want to tackle its "issues".
Education of volunteers and donors is so important, but there are people who are "walk on" one time donors who don't get the message, and face it, there are people whose standards are very low. Do not feel bad if you have to discard donations.
At the risk of sounding heartless, I will tell you that I regularly repair charity afghans made by a sweet blind lady and given to our group.