I think one thing we are over-looking is what type of washer you have. Those with the old style agitator or top loading, will experience more strings without a doubt. This style machine is much harder on your fabrics, clothes, etc. than a front loader.
I currently have a front loading which is way more gentle on the fabrics and do not experience this problem. I have found the cheaper fabrics will fray more or the more open weave fabrics. Food for thought.