You can mix them. However, it's a good idea to do a moderate amount of quilting so that the batting controls shrinkage. If you tie, for example, different fabrics have the opportunity to shrink or not shrink in different amounts.
I would test any suspicious fabrics for bleeding. Drop a small piece in a glass of water and see if any dye bleeds into the water. Rub the damp fabric against light fabrics that will be used in the quilt to see if any dye transfers. Most fabrics are colorfast these days, but it's possible to get just one bleeder that can ruin everything.