There are many cottons and some wools that can be machine washed and dried. Wool yarn that can be machine washed/dried is called “Superwash.” Also, merino wool is very soft, much softer actually than most acrylics.
Generally acrylic is not a good choice for socks because it tends not to hold its shape well and doesn’t breathe, making feet too hot and sweaty. However, that may not be as much of a consideration for babies who are not walking around yet.