'Eco-friendly' is often just a PR term, like 'natural' or 'organic.' Higher-quality sheets often come with independent certifications, which help verify the label isn't just marketing spin. Some fabrics, like Ettitude's bamboo fabric, are certified to Oeko-Tex standard, which certifies they're free from harmful chemicals. This is a good one to look out for, but organic options are also ideal for skin sensitivities, allergies, or eczema. You might also see sheets certified to 'Global Organic Textile Standard', like the Blessed Earth sheets.
Independent certifications are usually difficult to get, and organic fabric certifications like GOTS require that fabrics are grown and produced according to strict guidelines. Even with this accreditation, sheets can still be produced in a way that's harmful to the environment. Viscose rayon sheets made from bamboo, for example, can be produced with a solvent that causes air and water pollution, as well as health issues for the people making the sheets.
Lyocell, or TENCEL, used by companies like Koala, is considered to be a more environmentally-friendly way to make fabric. This method dissolves plant pulp and spins it into a strong cellulose fibre, which is much easier on the environment than other fabric production methods. On the other hand, it can be pricey. Microfiber is much cheaper, but synthetic threads cause water pollution as you wash your sheets. If you're eco-conscious, it's worth making a bit of an investment when it comes to sheets.