Vinegar is a natural fabric softener. Soak your socks in a (white) vinegar solution (1/4 cup in a gallon bucket) over night and then wash as usual.
It’s how I’ve softened stiff 100% cotton jeans in the past.
Warning: this ruins anything with “stretch”. The vinegar breaks down the elastic. I’ve ruined some really nice jeans with this method. RIP.
Your comment is how I found out. Damn.