Your choice. I am a mix of both. Being small and attractive, men always seemed to like to protect me and extend those niceties like opening doors. I was raised never to chase a boy and although I don't judge women who are comfortable with that, I am 51 years old and have never so much as asked a man to dance. It's not something I'm comfortable doing.
We differ in the provider category. For me, whoever is stronger in that category does it. I've always been able to provide for myself and have been the breadwinner in several relationships. That said, as long as the man is doing something to contribute, I'm okay.