I think I would cut a couple of strips of the red and put some of the other fabrics you plan to use with it on top of the red (or under it - just so they are touching!)
I would dampen the whole works and let it set for a few hours and see what happens. If the other colors do not pick up any red, you are good to go.
However - if they do pick up some of the red dye - some people would treat the red with Retayne - I would toss it - or ONLY use it for something that would not matter if red dye spilled on it.