I picked up a trick years ago from my aunt who has 8, yes 8, kids.
I have my family trained to pin their socks together with a medium safety pin before they throw them in the laundry hamper. If one is not handy, fold the tops together so they don't separate and I will put a safety pin on them before they get put in the washing machine.
That way the socks always come out pre-sorted in pairs. Just need to sort by person. DH is easy. DD8 has smaller feet, so hers are easy. DD11 and I wear the same size. Mine are plain white. Hers are white with a band of color on the top. We have no problem wearing each others sock if needed but they do get sorted by the color band into our own drawers.
Yes, there have been occasions were the safety pin comes loose in the machine but only a handful of times in 13 years and a gazillion loads of laundry. I do inspect the safety pins when putting them on or removing them to make sure the head isn't pulling loose and pin in danger of popping out.
There have been a few times when a pair of socks manage to make it into the machine without being pinned together and 9 times out of 10, the machines eats one of the socks and it comes out an orphan.
The family knows I'm fanatical about always keeping the socks together. It was my job as a kid to pair up all the family socks and I ABSOLUTELY HATED IT!

Never again!
It's not that hard to do. When you take out a clean pair of socks, there will be a safety pin, pinning them together. Take it off and pin together yesterday's dirty socks before throwing in the hamper. I also keep a few extra pins on everyone's dresser and in the laundry room. They HAVE to go into the machine as a pair! LOL.
We also have an orphan drawer for the clean socks that had a matching pair go missing. Even with a seemingly fool proof system like mine, it still happens! Every time an orphan sock comes out of the dryer, I check it against the ones in the orphan drawer. After a few loads of laundry, they eventually have a family reunion.

After a while, the true orphans get recruited on household cleaning missions. What a sad fate...
