I machine wash my poly/cotton, PV, and poly/wool kilts, tumble dry on very low heat, and then press if needed. Repeated washings and no ill effects with any of these.

My 100% wool hiking kilt (used band kilt from eBay) was looking pretty dingy, so I used the cold tub technique with Woolite. After rinsing, squeezed as much water out as I could, then hung up to air dry, squeezing the lower edges a few times as water accumulated there. Pressed with a dry cloth while the wool was still damp. No shrinkage, no damage, colors are more vibrant than ever (it was used and probably never washed before I got it).