It sounds to me as if leadership is an issue in this group. If the group and its leader have a clear understanding of the standards of the recipient organization, then decisions can be made as to what supplies to keep.
Leaders can quietly and possibly gradually go through the stash, removing the unsuitable items. And from then on, be at the incoming door when new donations come in, so that they can be sorted through before other people see them.
We must always be understanding of peoples' history and circumstances. There are different possible reasons why people think that "everything" should be used. It could be that they have suffered scarcity in their lives. Other people simply have a need to keep things. And in the case of charity work groups, there may be some inexperienced people who just don't know much about textiles.
It is always a challenge to do charity quilting with a group, but with good leadership, it can be a rewarding experience where people grow in many ways.
Dayle