I'm anti white sheets, which is apparently a minority. I would pretty much do any color except white. I personally like light green or blue.
Another anything but white person .... I've got everything from chalk to navy to plaid. From what it sounds like- wish family, twin bed - I'd go for something light gray/blue/green.
My friend is executive director of the organization so I finally just emailed and asked if she knew. She asked the mom and it turns out it IS for a kid and dark colors or kid fun patterns are preferred. Dinosaur sheets here we come!
I have a friend who works with people transitioning to apartments after being unhoused or in shelters. They always suggest color for things like sheets, socks and underwear as money/laundry access is limited and they won't generally have the luxury of sorting by color.