You can test by taking a small piece from each fabric (about 1-inch square is enough) and placing in water for a few hours to see if it bleeds. Afterwards, rub a white cloth over the wet fabric to see if any dye "crocks".
I don't usually do this. I probably would if I were mixing reds or blacks with whites. All I usually do is wash the quilt in Synthrapol the first time.
Even Synthrapol won't stop a heavily bleeding red fabric from tinting other fabrics so, to be on the safe side, you might want to test any dark red fabrics. Just from clothing, I have noticed that blacks are often not stable too.