Well, I solved a mystery today. My camera seems to always get dirty while I though I was being very careful. It turns out, it is the camera strap. After shooting with it in extremely hot and humid weather, sweat, sunscreen and insect repellent dripped from my neck into the strap and now it is making the camera rather sticky, particularly the LCD screen as the strap naturally lands on it when stored.
These are not the included camera strap but a very padded type from Zeiss and Leica. I've been using these for years and feel that they are life-changing since they allow me to carry my camera for much longer. It is made of neoprene, nylon and rubber.
How do I wash such a strap? Can I put it in the laundry machine? If so, what settings?