Safety while camping has much to do with whether adventurers are traveling solo. If traveling solo, women need to take the same precautions as men, but maybe a few more too. As mentioned earlier, traces of man's encroachment on nature will certainly be found in all but the most out-of-the-way places. With the number of established hiking trails opening up, the floodgates have also opened for plenty of crazies and kooks as well.
The best advice is to stay away from people encountered on the trail who make you feel uncomfortable in any way. This goes for solo campers and hikers, and everyone else who ventures into America's forests. It's a good idea to avoid divulging your route or plans to anyone who isn't an official. (Be sure to leave an itinerary with friends and family.) Camp off the beaten path when possible; if anyone stops and seems overly inquisitive about your trip, fib about your plans. If all this sounds suspicious and antisocial, aren't you trying to get away from it all anyway? Why introduce urban ills into your Midsummer Night's Dream?
A word of warning: be safe when you are camping in bear country. You'll have to suspend food, garbage, and pots and pans from a rope in the trees. Always do this - an assault from a hungry bear can be dangerous. Suspending food will also deter other animals seeking a free meal from your campsite.