Bob makes a good point. The most important thing for a dancer is to feel the floor. Cotton socks tend to be bulky, and can limit the feel of the floor.
The natural alternative to synthetic nylon and natural cotton is the natural silk. These can be expensive, and have a very limited life-time. Winter Silks makes silk socks at a reasonable price, compared to some alternatives like Orvis or Madison Avenue stores.
If you take care and clean and care for your feet, nylon is an acceptable alternative. But if you want natural fabrics, silk is the only one left.
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