Krellin, let me use a poker analogy to explain why you are right, but also wrong.
When I sit at a poker table the people are more important than the cards and I have to play them rather than the cards in order to win. Poker is also a game of limited imprecise information. Now suppose an unknown woman bets into me on the flop and I need to access if she has a made hand, is drawing to a hand or is bluffing. I look at their appearance, how they stake their chips, their age AND their gender. Women tend to be less risk taker in my experience and is supported by evidence such as more men file for bankruptcy. Older people also tend to be more conservative. If the decission is borderline I may be swayed be the fact that the better is a woman.
However, I went to a poker tournament this weekend and the seat draw was posted on line prior to the day. I ran my table through a database to see how much money each player had earnt. Of the two woman on my table one didn't register at all, and after an hour of playing it was obvious why, and the other was very successful and again her play re-inforced that she was a more than competent player, she did get unlucky, but her play was solid.
What this illustrates to me is that people can make certain assumptions based on stereotypes and in the absence of better information, they may be acceptable. But if you have better information which allows you to adjust and adapt, then you should use that info and not get tied to the stereotypes. In poker that could cost you money. In life it could cost you much more.