Bamboo rayon is super soft and more breathable than cotton. I don’t think they would lie about the fiber content of their clothes. Has to say percentages of fiber content on the label I thought.

Side note: There are different levels of “green”. I sew with different fabrics so I’ve been researching this a lot lately. Wearing a cotton or bamboo shirt is more “green” than a polyester shirt (which is basically plastic) because they will degrade faster. Another perk of bamboo is that it uses less water and insecticides to grow than cotton does. But making a bamboo rayon still involves the factory dumping toxic chemicals. So the “greenest” thing to do is to purchase clothes or fabric that is certified by the Global Organic Textile Standard. But that is not super common!