I remember once having five pax (all the same party) refuse to get on the aircraft when they say a female sitting in the left seat. They later agreed to fly subject to the other pilot (me) taking command. They were escorted to the door with what could be desrcibed as a certain lack of respect.
On the one hand, it is absolutely true that some of the larger airlines have occasionally hired women under pressure to be PC (I have that first-hand). On the other hand, it is also true the women often need to prove themselves more thoroughly in training. I doubt that, on average, a clear advantage exists.
What has hurt the cause of women pilots, is the few who have failed courses or checks, and then screamed discrimination. This makes airlines VERY wary indeed. The other thing that makes airlines very wary is the possibility of pregnancy!
The worst aspect of this whole subject is the few women who wear their feminist credentials next to their wings, and make life miserable for every male pilot unfortunate enough to fly with them. Luckily, such folk are few and far between- but they do exist.
In my experience, both in training and everyday line flying, I have enjoyed immensely working with female pilots. Most of them are excellent and in a lot of ways, display a better temperament than men, not being so prone to taking risks or "pressing on".
Finally, It completely escapes me why there are so few women in aviation. Given the physical and mental requirements of the job, I would have thought thousands of women would have been doing it.