Getting sweat stains out of hats is beating me

Depends on the hat. Baseball caps: hand wash, not the machine. Soak in cool water with a bit of oxygen bleach or dish soap, scrub the band with an old toothbrush, rinse, and dry it over a ball or rolled towel so it keeps its shape. Check the label first - older caps can have a cardboard brim, which water ruins. Wool and felt hats are dry-clean territory.