I agree that the acrylic and cotton yarns won't play well together in this application. I've made several string bags and the cotton is very sturdy, and doesn't stretch hardly at all... it's the knit that makes it expand to hold about half a cart full of groceries. The baggers at the market are always impressed.
I've made about 4 with hemp yarn that's also sturdy and non-stretchy. They're beautiful and strong, but the yarn for each bag ends up costing about $40... yikes! SnC is a much more cost effective option.