There are several non-organic mulches:
-membrane: black plastic or fabric
-stone or gravel
-rubber chips
Red bark is an ORGANIC( meaning made from a living thing) mulch and safe. If you mean red coloured rubber chips to simulate red bark, I will say that if you love your garden then by using rubber mulch you will kill the thing you love. It's sickening smelly when warm, and it has zinc, cadmium and other toxic heavy metals. I've seen it layed down in children play areas and think that is a big mistake let alone in a garden. Now if you are referring to the red dye used to colour the wood, it is vegetable based and safe. I think that in this case the type of wood used would be more of an issue than the dye used to color it. Welcome to GOY!.....giving a location (you dont have to be too specific even a growing zone will do) will be helpful in answering any further questions you may have about your garden.