Woman here. No, I do not believe it's safe for women to hike alone. While most men in the western world would never harm a woman, women are magnets for the minority who would, and there are enough opportunistic predators out there that women find themselves being assaulted at the most random times while trying to perform the most mundane tasks.
I don't think the good guys out there really are able to understand what women actually face with regards to their safety, unless they have daughters, but I don't fault these men for their lack of insight and understanding. In most instances, as they are good guys who are down right disgusted by the thought of a man hurting a woman, they just really have a hard time fathoming that there are any non-negligible quantity of guys out there that would hurt a woman at all. And they don't have the life experiences of a woman to show them otherwise.
I spend 95% of my time surrounded by men, often in primarily male environments, and with that in mind, the number of times I've been threatened or harassed in some way by a man, for the fact that I am a woman, is small. However "small" is not "zero", and it only takes one instance of violence to harm or kill or victimize you.
In my life, I've had random, often much older men try to coax me into their car on more than one occasion, and men online send me unsolicited photos of their genitals on countless occasions. I've been harassed on public transportation by men who have approached me to say sexually explicit things, and have then proceeded to follow me and would not leave me alone until crowds scared them away. I've had men become hostile because I've told them politely that I wasn't interested (one told me to "f#ck off and die"), and one acquaintance, who thought I had rejected when i informed him that I was busy on the day he had asked me to go out with him on, responded by tossing a full cup of ice out the window at me from a speeding car. I've had guys say "Hello" to me on the street as if they were nice, respectable people, only to start harassing me with sexual suggestions when I was kind enough to say "Hello" back. And this was in a city where, sure, you run into more people, and thus more bad people, but a lot of them are inhibited by the crowds.
But what if I were to run into one of these guys alone in the middle of nowhere? What is to stop them from going as far as they want?
I will level with you all. I'm 5'2, 127lbs and have trouble benching the bar, which is 40lbs. At my strongest, with serious training, I could never bench more than 65lbs. Do you think I could easily subdue the average sized man? Women do not fight men off with their strength. When you hear on the news that a woman managed to fight off her attacker, what actually happened was the woman made a commotion and scared the attacker off because he was afraid other people would come see what all the commotion was about and find out what he was trying to do to her.
I'd love to live in a world where I did not have to deal with these issues and had the same freedom to explore on my own without the added liability that being a woman presents. Heck, I'd even settle for a world where taking the trash out at 2am wasn't something that forced me to ask myself "Do I take the trash out and risk getting raped? Or do I put up with the smell until morning?" but that's just not my lot in life.