Normally, no, I do not get nervous at all going out as my female self in public.
There are a few rare exceptions. I am a retired engineer (electronics), and our field is still mainly male dominated. I attend a few technical gatherings every year and one or two conventions, and I even speak publicly at one. All of which I do as my female self. Many know I am a CD and many do not. Thus, I always find myself as one of the very few women, if not the only woman at these events. I make it a point to dress professionally and conservatively. Nevertheless, I often do feel a bit tense, knowing many male eyes are on me. Moreover, the males are wondering why is this female at an engineering gathering. Then you see them attempting to move in closer for a look at my name tag. Too funny!
At the one event where I speak, I usually open with a joke, making myself the subject of the joke. That tends to put everyone, including myself, at ease.