Is it being old fashion or simple courtesy and respect?
I agree, modern times have distorted our approach to courting. A door being opened, dressing for an occasion or pulling a chair out.
I try to practice these things as regular behavior. I am female but I will hold a door open for either sex. If there is a special occasion such as a date or finer restaurant, I will dress for such an occasion. By making an extra effort, in my mind, that makes the activity more special, even if the other party doesn't notice. If my efforts are lost on my date or a stranger, I don't care. I will continue to do it.
In my mind, equal doesn't mean rate of pay or title. It is paying respect to both sexes equally. If one doesn't appreciate these things, they may have not learned common courtesy. Their loss.