As stated earlier, many synthetic materials work great. In my experience, not much wicks moisture better than base layers made with synthetic fabrics.
I currently own about six or seven wool sweaters of various weights and colors, along with a half dozen wool shirts (famous company in Oregon). All of them were purchased from thrift stores for $6 or less, including a sweater with the manufacturer's tags still attached. I did break down and buy a camo wool sweater with a windstop type lining (synthetic) and hate to take it off. It is extremely warm and quiet when going through brush. I think wool is as quiet as any fabric when going through brush.
I love wearing wool over synthetic base layers, whether I am hunting, ice fishing or cross-country skiing. And I am not giving up my boots or waders with their fancy synthetic, water-proof, yet breathable liners. I really like the look of Ron L's wool. Need to save some money.
Compound shooters place their faith in modernized versions of bows, so an affinity for modern fabrics seems to be a consistent pattern. Also, synthetics drop in a washing machine, whereas my wool garments are either dry clean only or wash by hand, which is a little more effort.
For what it's worth, none of my recurves or longbows have sinew strings; all are dacron or fast flight. Does that violate the spirit of traditional archery?
As for the fire hazard, I don't intend to burn up any time soon while hunting. However, if you check military blogs or many of the sites that tell you what to send to our troops in Iraq and Afghanistan, you will find that synthetic clothing has been banned from combat use. Many burn victims from IEDs have had extreme, and in some cases, fatal injuries due to melted synthetic clothing due to subsequent fires, which led to DoD's ban. The melting hazard is real.