I use Tide (no scent) for all of my bike stuff- wool included. I also put about 1/4 cup of white vinegar in the rinse (in the fabric softener cup of my machine). I never use the dryer for my clothes, just hang them up after the wash.

I've been using this method for washing all of our clothes for about 20 years now and haven't had any problems. However, since I live in the SF Bay Area, we are blessed with reasonably soft water so that may help.