The criticism around Lena Dunham's Girls takes two different, overlapping, forms: criticism of the fictional protagonist modeled to some unknown extend on the actual life of the auteur, and criticism of the fictional portrayal of the shallow or blinkered. These are difficult to parse because the first set of issues are longstanding; people have genuine difficulty in separating writers from their writing, artists from their art, etc, and the tendency to read fictional output as personality simpliciter is frequently enacted--see Woody Allen, Kanye West, and most biographies of literary figures. The second is part of a set of issues about what, and how, fiction is supposed to work; there is a particular sense that now there are a greater number of unlikeable characters, that this unlikeability is a way of signifying 'realism,' and this realism is expressed primarily through the grim, the awkward, and the mundane. In the case of Girls these issues are heightened by considerations, alternately facile and serious, about the role of women and/or people of color in fictional worlds (the pushback on Jeffrey Eugenides' The Marriage Plot is another example of this ongoing conversation with respect to the role of women). Lastly, one must say that Lena Dunham does not always appear to be her own best advocate.
Well, no one, to my knowledge, thinks of Alexis Bledel and Rory Gilmore as being the same person, and while auteur Amy Sherman-Palladino certainly writes with one very typical type of voice, Gilmore Girls nicely divides up its concerns between a wide variety of women, and finds the time to validate many of their own particular choices and beliefs. It's fitting rather than reductive that Lane inherits her mother's values--people tend to end up like their parents, more or less. Sookie gets pretty much what she wants. Paris might be a pain, but she's an endearing one. The way the latter seasons suggest that Rory draws her personality most strongly from her grandmother are well-observed. All that as preamble, let's get down to business:
The show is a real drag once Rory gets to college, if not sooner. That she would find Logan and his gang of rich folks to be enjoyable is not surprising--the freedom that comes with money is a real kind of freedom, after all--and that she would enter into a relationship with the least suitable of these and eventually decide she didn't want to be with him also seems realistic. She also steals a boat and drops out of college, and spends a significant amount of time being a general dirtbag and mean to anyone who wants to help her. Of course Lorelai takes her back--motherhood is about nothing if not infinite forgiveness--but the whole thing is unpleasant to go through. So also the slow process by which she discards her first boyfriend--infinitely patient with her, as it turns out, and working so hard to avoid trying to change Rory while also carving out time for his interests--for the pseudo-literary bad boy who just feels too much to subscribe to your middle-class notions of 'acting like a regular human being,' man, is also realistic, and also uniformly unpleasant. Anyone who was in high school will recognize it as A Thing People Sometimes Do. Why anyone would want to relive this particular set of emotional experiences is baffling.
Rory is a character who is quite plausibly drawn as both very intelligent and poor at making decisions, particularly about relationships, and this seems like a plausible combination of traits. But the question is not whether they're real, but whether these mistakes are dramatically interesting, especially when she repeats the same mistakes--choosing someone who is unable to clearly articulate his feelings, who is ambivalent about the nature of their relationship, someone who is in some relevant sense a bad person (if not an evil one). The defense usually offered is that these people draw Rory out of her shell, and this is a good thing, but the series itself raised and answered this question in the first season episode where Chilton gets concerned she is not active enough socially. In that episode, it eventually resolves that she is perfectly fine as she is: she has friends, and makes new ones, if at a slow pace, and wanting to read, etc, is a perfectly fine way to go through life. However, the adventures of someone who is fundamentally well-adjusted to life, but introverted, lacks dramatic spark, so it must be brought in from outside forces; in order to bring the same spark, these outside forces must become progressively stronger (also following the rule of patterning or matching and intensifying in a television show), and thus the reasons for the show's well-accepted slide in quality during later seasons. It is a short-term attempt to goose the dramatic value of the show, with the benefit of being a realistic depiction of the poor decisions made by a very smart young woman, but is generally recognized as a creative failure.
Gilmore Girls, then, is a show whose titular characters are often the least interesting, and whose conflicts, even when believable, are both realistic and unpleasant. It seems entirely possible to say that it is a success in its aims, and not very much worth watching through to the end.