Natural Clothing “Exclusive of Decorations” and the Toxicity of Dyes

I am trying to find cheaper, post-baby, all natural clothing to wear, some to exercise in. It's not easy to find all cotton work-out clothing, but Champion does make cotton clothing that is pretty cheap (esp. on sale). However, it is 100% cotton "exclusive of decoration." I assume this "decoration" to be the small "C" embroidery on the clothing items. Is this still okay to wear? How do you know if dyes used in cotton clothing are safe?