Quote Originally Posted by beloitpiper View Post
where women want to be treated the same as men.
Ah, and therein lies the rub.

Although I must admit it has been quite some time since I was "scolded" for opening the door for a 'lady'. As for the hat tip, when introduced while wearing a cap the most common for me is to remove the hat entirely, barring that the thumb and fore-finger to the brim as several others have mentioned.