The problem is mold and/or bacteria that grow in the moist environment of the clothes. I’m not sure you could add anything to the water that would really fix this, assuming that you always the clothes rinsed at the end with clean water. Even from a sterile starting point, these critters will float in on the air.
If your final rinse contained an antimicrobial agent, you’d be wearing that against your skin… I don’t think that’s a good idea.
They don’t do this (as much) in a glass of clear water because water doesn’t have any other nutrients. Clothes do. Even if your clothes were perfectly cleaned of everything but fabric itself, most fabrics are digestible to these microorganisms. Wool and cotton are just plant and animal fibers, for example.
I just don’t see any solution but drying them as quickly as you can.
I’ve had good results with my colored clothing loads by adding a dollop (sorry, that’s as accurate as I can get without measuring) of bleach to the water while it is filling up for the wash cycle. I make sure it is thoroughly mixed before adding any clothes, and it does not fade or stain them. Anecdotal, but I have noticed that if I forget to transfer those loads to the dryer and they sit damp in the washing machine for a day, they tend to stink much less or not at all compared to briefly forgotten loads where I didn’t add bleach to the water. My whites never smell after sitting damp for a day, and they get considerably more bleach.
I have heard this answer before as well. It only takes a capful of bleach to kill bacteria and it (supposedly) has and imperceptible effect on clothing.
You might reconsider your choice to not buy a clothes dryer.
Let’s say that you spend 15 minutes every week hanging clothes up on lines to dry.
Let’s also say that you can read a page in a minute.
Well then, by saving time from hanging clothes up, you’re gaining 780 pages worth of reading time every year - quite sufficient to work on advancing your career by self-educating yourself in related topics.
So say that you can earn an extra $0.50 an hour if you do that. In 800 hours of work (20 weeks), it will have paid itself off. And your clothes will be fluffier.
I have this problem sometimes, but usually only if I leave the laundry sitting in the machine or in the basket for too long before hanging it up.
If hanging stuff up inside at night, I sometimes leave a fan blowing on it (standing type).
Spacing clothes apart is also important. Are you perhaps hanging them too close to each other?
(I’ve actually gotta go hang up the laundry now. The machine just beeped at me.)
On days when the weather won’t cooperate, hang them indoors, in a room with a ceiling fan running. If you go out, turn the fan to the highest setting. They’ll dry just fine, no musty smell!
I use a dryer but have had odor problems with freshly laundered clothes.
My washer and dryer are in the garage and I live in a humid climate. If I’m getting ready to have a laundry party, I run the load of whites with bleach first. I’m pretty sure the odor comes from water and/or moisture that has collected or been sitting in (perhaps the waterline to) the washing machine since that last time it was used.
Doing the whites with bleach first eliminates the problem.
Neglected is the capital and operating cost of the dryer.
Also, perhaps he hangs most of his clothes on hangers in his closet; he would need to spend the time hanging clothes whether it’s straight from the washer en route to the outside, or, from a dryer.
I do agree about fluffier clothes though.