The best female pilots are the ones that have nothing to prove. I don't know you personally, and I've never flown with you, so I don't know how you interact with other pilots. But if you go into the cockpit with the attitude that you should be treated any differently from a male pilot, it will show through your actions and interactions. As a result, that can result in the various responses (from other crewmembers) that you described.

Do your job and have fun, but most importantly be professional. If you go in and try to be buddy, buddy (particularly as a new FO), it can result in uncomfortable situations.

That said, there will always be an odd interaction, at least until you gain some familiarity with the crews you fly with, or more women enter the profession.

Finally, I know (and have flown with) many female pilots. Many I respect. Those that I do are darn good pilots, but they also don't fly like they have something to prove. They're confident in their own abilities, and it shows through their flying, not through their talk. On the other hand, there are those that fly like they have something to prove. Always nitpicking (themselves and others), and usually uptight and not very friendly. That can make for a long trip.