Male Fashion Advice

Depends on the material moat likely, but for cotton/linen/synthetics that I wear Fast Orange and other degreasers work really well without damaging the material. I spray it on and leave it for a few minutes, scrub a little and then toss it in the wash. There is probably a clothing specific comparable product that is actually safe for more fabrics, like Oxy Clean which I use for stains from foods and liquids.

If it is from detergent buildup then you are using too much. The recommended amounts tend to be higher than you actually need for day to day wear.

It is important to know what is causing the rings first.