Or look at it this way: If this show was called Guys, and its showrunner/protagonist was in every other way similar to Dunham/Hannah—a dorky, slightly overweight guy who bumbled his way through Brooklyn, trying to find his purpose and working his way through a calamitous love life—would any of these criticisms have popped up? Would the people being uncharitable toward Girls have been uncharitable toward that series?
The intended answer, provided in the example given in the rest of the quoted paragraph, is 'no, they wouldn't.' But this is certainly wrong: fat schlub/attractive woman shows are a television staple, and no one hesitates to make fun of them when they bother to watch them. Or: Adam Sandler has a new movie coming out (apparently): what do you imagine the odds are that he'll be paired with a woman significantly more attractive than he is? Do all the criticisms leveled at Lena Dunham also get leveled at Adam Sandler? Probably, with the exception that people recognize Sandler is inexplicably popular and just makes the same sub-par movie with his friends over and over again regardless of what critics say.
This is not a judgment on the quality of Girls, which I have not seen, and may well be as good as people claim. It's also not a comment on criticism that relies on attractiveness as the relevant standard for entertainment, rather than quality: people who don't like a show because they think the lead is not attractive are not savvy cultural consumers, at the very least. But it seems to me that people are tired in general of the life stories of slightly dorky people, in Brooklyn or elsewhere, attempting to work their way through life. (Consider whether you'd want to read a novel or--heaven forfend--a memoir written by such a person).