When you mention shedding are you talking about lint buildup in your machine? Or are you talking about problems with fraying?
I love Kona solids, and have used them a lot. If you're talking about lint build up then I can say that I haven't noticed any more with Kona solid colors than with the better quality printed quilt fabric I've used. I haven't used much red, but have used a lot of the black, various blues, whites and grays.
I have noticed in other lines that different colors of the same line can cause different amounts of lint and I don't know if Kona cotton solids have similar variation.
If you're talking about fraying then I would say that I have noticed less fraying with Kona solids than with other solids, they tend to be a bit heavier weight and more tightly woven than some of the other solids I've purchased over the years. They also tend to be a little heavier weight than some of the good quality print lines as well.
Rob