Anyone can be a mystic. I think it is harder for men in general. They are not as sensitive.
Even worldly people (who believe it exists) know that mysticism is not for the faint of heart. Very few can be a mystic. Just from a cursory look, most saints did NOT have those powers. It also seems like more male saints than female saints delved into it. Probably because a woman's emotional state can more easily interrupt the process.
I do know the "mystics" in other religions almost always were women and the legends and testimonies involving them were definitely not under God's protection. The oracles of the ancient Roman and Greek religions were an example. Even today we see psychics, fortune tellers, and palm readers seem to be overwhelmingly women. Being sensitive to the spirit world is not necessarily a good thing. If you can't use it properly, it can really wreck havoc.