I'm in a really hard water area and find that fabric softener helps this problem. I've always used either Comfort Pure, or Fairy - no problems with either of my DCs. (The time I used bio wash liquid by mistake is another story! )
The only things that go really cardboardy are towels, and DH's jeans (not mine, for some reason). I just give them a really good shake before folding. Maybe 5 mins in the dryer if I'm feeling extravagant.
A water softener like Calgon in your wash helps, but not sure if it's eco friendly. I use that alone on towels once in a while and it de-crunches them beautifully! I think white vinegar can be used in the same way.