Socks are not the most sustainable brand of clothing, because nearly all (even) organic socks still have a small percentage of elastane (used for stretch and comfort). So unless you can find 100% natural fibre socks, launder in a microplastic catcher.
Get together as a community and order a one-off TerraCycle Fabric & Clothing Box. Fill with all your socks, fabrics, textiles and hosiery and send it off (using the prepaid) label to recycle into other things.
Keep socks away from pets. This is because they smell lovely to animal friends, but can cause choking, constipation and intestinal blockage. Signs of sock ingestion are lethargy, vomiting, loss of appetite, a tender abdomen and difficulty pooping.
Eczema Clothing (also for men) is a company that makes 100% cotton clothing for adults and children with eczema or similar skin conditions. For this reason, these socks are free from irritating toe seams, and made from organic cotton. They are free from latex and elastic, the socks held up purely by the ribbled knit around the ankles. Due to high cotton content, these socks do stretch a little on wearing, but regain shape after washing. Manufacturing technical requirements means there are one or two (very thin) threads of elastic thread at the top, which can be removed if needed. Note their knitted thick socks do contain a little synthetic elastane.
Ecooutfitters produces Teflon-free organic cotton school uniforms, and also offers 100% organic cotton ankle socks. They are soft and lightweight, with a fine rib that’s ideal for children with sensitive skin. Again they are free from latex and have no elastic around the ankle. Sizes are clearly marked on the soles, to easily sort after washing. Made in Portugal.