I've seen prayer shawls for girls available on the internet e.g. for Bat Mitzvah. I'm not sure what to think of it or if I'm comfortable with it. Can a woman wear a prayer shawl, and if so under what circumstances?
The Torah commands to attach tassels (or "fringes") to the edges of any four-cornered garments we must wear; however this only applies during the day, not night. This makes it a "yes-do" command that's limited in time. The rule of thumb for this category of commandments (which also includes shofar, lulav, and the like) is that women aren't obligated in them; however it would be meritorious for them to choose to do so. Sephardic women do not recite a blessing on such actions, Ashkenazic women do.
When it comes to prayer shawls, however, there was one opinion from the Talmudic era that because it's an item of clothing, it inherently becomes "a man's garb" and prohibited for women to wear. (The Torah prohibits cross-dressing.) We generally don't follow that opinion, but it is a cautionary note. Many are of the opinion, however, that the standard black-and-white model may be problematic as "men's garb", so something more feminine-looking is preferable.
The biggest issues are what we'd call the "meta" concerns. Is a woman wearing this saying "G-d I'm not actually obligated to do this, but I like doing something extra", as part of a well-balanced range of religious activities, or is this a big political statement to show everyone else that there are no differences between men and women?
In short, if a woman wants to wear a prayer shawl:
I've shared your reaction in the past. Interestingly enough, it seems that Posekim in the last century (who disapproved of women wearing one at all) preferred that if a woman were to wear one, she wear one that is distinctively feminine in its design.
I cannot pull all the necessary sources at the moment, but the basics are as follows:
The Shulhan 'Aruch writes that:
The RaM"A adds:
This point about false piety is taken very seriously by R' Moshe Feinstein, who stated that there are clearly multiple issues at play. Since women are exempt, their decision to adopt the Mitzvah needs to be done for the sake of the Mitzvah, not for the sake of being like a man. In a similar vein, since women are exempt, the very nature of the act of donning a garment for a Mitzvah in which only men are obligated kinda makes that garment a masculine garment by definition. As such, a truly pious woman, who decides to do the Mitzvah for the sake of Heaven, ought to wear only a garment that is clearly feminine in its design.
RM"F comes down strongly against women doing it at all, since most women who did so, by and large, were part of movements pushing women's egalitarianism, while at the same time pushing aside most Torah observance that was actually required; today, I personally still think he would oppose women's performance of the Mitzvah (except, perhaps, in exceedingly rare instances), even among women who keep Halachah, since, again, most women who want to do it are doing so in an effort to push egalitarianism much more than for the sake of the Mitzvah. But, again, if a woman were to do it, he'd require her to wear a feminine-looking garment.