My own anecdotal observation is that girls who are smart are fine-- girls who are TOO SMART, on the other hand, tend to be
not fine, socially speaking.
Girls are still (culturally-- and this is something that is also seen in transplanted cultures that otherwise produce gifted girls too) cautioned to be "modest" and "gracious" and "socially nice" rather than "bossy" or "aggressive" or other things that are seemingly okay for boys to be/do. Girls are taught, from a VERY young age, that making other people comfortable is THE job for them, socially. They learn it well. Gifted girls have learned to hide by the time schools go about identifying them.
I hesitate to use the hackneyed term "patriarchal" but that
does seem to be what it is, at the root of it.
That's my take. I also think that parents are more inclined to see passionate/assertive imaginative or excitable play as a "boy" thing, generally. In girls, it's seen as possibly ADD, selfishness, or just "flighty." They also get shunned by gender-conformist female peers if they have more androgynous traits/interests (and most hg+ people do), and quickly learn that there is a tremendous social cost to being themselves.
If you happen to have a highly gifted girl, the best advice that I can give is to let her know that while dumbing down in social settings is a valid CHOICE, and that you respect that choice-- there are down sides, too. The fact is, though, when they reach adolescence, it's a lonely place, being a gifted girl. The girls don't like you much because you're one of the guys, and the guys LIKE you because you're one of them-- and because you have cute friends and insight into what will work in dating those cute friends. You, on the other hand, get to be a sideshow freak-- a tremendous amount of fun to be around, but far too scary to date, unless you happen to find a super-bright romantic partner who isn't
threatened by the possibility that they aren't the smartest one in the couple...
Most bright people have something of their own ego tied to being competitive and bright. The brightest of them very often have it tied to being "the smartest" one. This makes the teen years rough ones for little porcupines, needless to say-- and girls are so, so good at going along to get along, and oh my GOSH, how many times have I watched my DD feign utter ignorance in front of a group of peers or friends. Sheesh.
Humor is a good tool for "matching" with potential friends and dating partners. For my DD, it's THE trait that she uses as a screening tool. It's that important to her. It is also a shorthand way of assessing processing speed and global ability, too. Handy, that.
What I find an interesting model among the first-generation immigrant families that we know is the N. Indian/Pakistani/Persian cultural tradition (and maybe it's unique to the area in which we live, or it's a feature of immigrant culture). In those families, the girls are often encouraged to be VERY assertive, VERY bright, and to not hide it for anyone. That is the community in which DD has found female peers in the largest numbers, by the way.
It's just plain hard. If you accelerate, then your girl is years younger than her high school/college classmates, looking down the road a bit. On the other hand, if you don't-- she's not going to fit in much better for being a decade beyond her peers intellectually (and possibly emotionally/developmentally). There
is no good fit until adulthood. That's the reality. I have a 16yo who is (developmentally) unwilling to date or hang out with the 18-20yo peers in her college cohort-- because
they are immature. 
Her attitude about the college party scene is that she doesn't need to experience it to know that some things are simply a colossally bad idea. Her peers don't really see things that way. She's all about consequences and can generally see them coming a mile away. They won't be on par with her in that respect until they are more like 25. Her friends tend to be seniors, the serious and driven high-achievers, and grad students. She is quite lonely, though college is by far the best that it's ever been-- she does HAVE friends, and doesn't feel like she has to hide how capable she is the majority of the time, anyway. She still does things that freak her peers out because most human beings cannot do them-- but mostly others accept it as quirky, rather than alarming.
Sorry that isn't more encouraging. Smart girls hang out with smart boys-- because there aren't groups of smart girls who are willing to BE smart. Nowhere is that more true than in middle school, incidentally.
