I can't speak for others. But from my personal perspective. "The" woman for me would be a woman that believes herself to be an equal to me. I find it really great to have a woman that's supportive and corrects any mistakes I might do. Cultural differences do exist and are a reality. However, in the current global environment we are living in, cultures are somewhat intertwined. Especially since most of us here live in the western world, where each us confront an array of different values and traditions on a daily basis, both within Muslims societies and outside.
I personally have been brought up in a what you could say "liberal" milleu. I was never forced to do anything regarding the deen or cultural practices. Perhaps this could have been the root for me trying to find an identity for myself, which alhamdulilah has shown me that the Deen is everything I would want myself to be associated with.I pray Salah, fulfill my obligations[ as much as I can] and never try to judge others or think myself to be better than anyone else.I have numerous acquaintances with people having different views of the world from Atheists, to Jews. We actually get into healthy debates, and I ended up having 2 extra Muslim friends who were formerly atheists. Up to this day, a visible amount of my friends are Reverts.
Our Deen is the root of multiculturalism, the root of free thought and speech, and freedom to conduct. So having Islam as your first and foremost identity is a great way of achieving a sense of ubiquity on how people see you. You'll be able to fit in anywhere. As it gives us that view to see things from different angles.
oh my... I just realized. That was boring rant. Sorry