Belief in magic is pretty even between the genders and pretty common
I was interested and looked up some studies. There is a gender gap in spiritual believe and women tend to be more spiritual, including believing in magic. So OPs statement in that regards holds.
Just to be clear, I'm not saying everything that op wrote is correct or that I agree, but the starting point they used, that women tend to belive in magical stuff more often, seems to be true.