If you are really in a fiery environment, you turn to yet another synthetic - Nomex. Working for the NPS, Nomex is required for wildfires - long sleeve shirt and pants, and also for helicopter work - the milspec Nomex flight suit or equivalent. In those environments, it is a good idea to be sure you are wearing nonsynthetic underwear and sox. Also pay attention to shoes and shoe laces - most modern lightweight hiking boots will degrade in significant heat (the glues holding everything together just melt). Leather laces are much preferable to nylon.

For normal use, I don't worry about it, although one of the biggest hazards is that an errant spark from the fire will melt/burn a hole in your super expensive, high fashion fleece.