Being a submissive woman was very culturally common in the USA until at least the 1960s. And men were taught to be respectful with women and appropriately aggressive. There are still many good submissive women and dominant men, however. In my opinion, most men I've ever encountered are somewhat dominant/masculine. As a woman just try to protect yourself when you are on the dating scene because there are a lot of cads out there.
A woman is only considered needy and weak when the man she is with is not really her match. When she is with a man that suits her personality there is no such critique, at least by him. Society and other people might always judge, however.
Just always be true to yourself, but protect yourself until you find the person you know you can be vulnerable with.