I would say YES, it's safe......women (either alone or in the company of others) have been backpacking all over the world, including the USA. They do it because they love the freedom, the adventure and the experience. These are your smart travelers and they do know what to do and where to go; what places to avoid, etc.
Now, for first-timers, I wouldn't recommend doing it solo! Not so much for safety reasons but more for practicality. More heads are always better than one when it comes to novel experiences. Backpacking is a hit or miss thing --- it's better to err on the side of caution...........at least, for beginners.
'been there, done that.....
Happy traveling!
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