I'm an American who never watched this show before but was generally aware of it through the decades. So out of curiosity, I tuned into the premiere and liked it immediately and especially the Doctor and have decided to watch the season. I have since read up on the details of the show and so have a general idea of what's going on and I have now seen Day of the Doctor (the War Doctor special) and part of Matt Smith's introductory episode. In general, the most exposure I've had now is watching Jodie's episodes and I think she's doing great. I love the show's and this Doctor's humor. Once she got past the obligatory "who the heck am I" stuff, the Doctor just comes off as a lot of fun, warm, very knowledgeable, etc.
A lot of the angst and negativity about having a female Doctor reminds me too much of the angst about Star Trek casting a female Captain for the first time as the series lead, or a black Captain for the first time. But, it sounds as though most have accepted Jodi and many of those who were reluctant came around. My feeling about the fact that there have only been male Doctors before so there can't be a female is that the real world politics/society made it so, and if the show had only started in current times, there would have naturally been more female Doctors. So it's best to just get on with it.