Water Heaters - Smelly Water

I am looking for some water experts that can assist me in a strange issue. I have an 8 year old home supplied with city water that has a gas water heater, a water softener and new clothes washer\dryer. My issue is kind of hard to explain so bare with me. Basically, our clothes and towels have a musty (mildew) smell once they are expose to moisture, i.e., drying off using bath towels or perspiration on clothes. Normally a bath towel will smell clean (fabric softener) after you dry off. But in my case, if you use a clean towel, which still smell like the fabric softener, once it get wet it smells like mildew. Same with some of our clothes. Once they are washed, they smell clean as they should, but in some cases the perspiration from your body makes the clothes smell like mildew. I started to diag the problem but by passing the water softener. Strangely this seemed to help. Granted this produced hard water, but the towels and clothes seemed to smell better after moisture. Now it wasn't completely gone but better. So, that is my issue and I am struggling for the cause.

Could there be something wrong with the water heater that is causing this issue? I am guessing not as this issue is also on towels and clothes that are washed in cold water only. Do I need a filter system somewhere in my water line? Any suggestions would be helpful.

Thanks

I moved your question here in hopes of getting you some help. The people on this forum are more likely to be able to help than those of us on the boilers forum.

My first suggestion would be to go to a detergent & fabric softener without perfume. Clean has no smell. Anything which smells "clean" really isn't. It is contaminated with some kind of perfume.

How about a filter system before the water softner?