I wash wool and silk using a ph balanced detergent with no protease. I use cold water, minimum spin, and a super long soak. Then I hang dry. It's more work to wash this way, but they last longer, never smell, and 100% silk and wool only need washing 1/3rd to 1/5th as often anyway, so the total work is lower than with plastic clothing. The brand of detergent I use is literally called "Soak," and I get it on Amazon.
The clothing comes out great.