Yes, gendered writing styles absolutely exist.
This study used samples of male and female writing to develop a predictive algorithm that could determine the gender of unknown writers with 80% accuracy. It was published in 2003 so there are probably more detailed and impressive studies available by now, but it's still notable for establishing that gendered writing styles are consistent across both fiction and nonfiction genres.
Essentially, the difference is that male writing is more "informational" and female writing is more "relational." Men use more determiners (a, the, that, these) and quantifiers (one, two, more, some) because they tend to talk more about specific features of objects. Women use more pronouns (I, you, she, her, their, myself, yourself, herself,
xir, xirself, theyself) because they tend to talk more about relationships between entities. In short, all the data seems to support the most common stereotypes about male and female communication.
Another observation the study makes is that the features of male writing and nonfiction writing are strongly correlated, as are the features of female writing and fiction writing. This can lead to some interesting quirks in male fiction and female nonfiction writing. Namely, male fiction has a striking tendency to include more "informational" passages despite the genre's overall focus on the subjective experiences and relationships between characters. If a work of fiction seems strangely preoccupied with the facts and history of its world, it is statistically more likely to have a male author. Likewise, female nonfiction has a notable predilection towards "relational" language despite the genre's focus on relating specific facts about objective reality. If a work of nonfiction seems strangely preoccupied with its author and the people whose facts it references, it is statistically more likely to have a female author.
This isn't part of the study, but gendered differences in writing styles may be why women are so commonly accused of having
"Girl on the Internet Syndrome." Obviously some women
do make lots of overt references to their gender in order to garner attention and favors, but a lot times you'll see presumably male users screaming "GOTIS" any time a female user references her gender, even when said reference is clearly innocuous and unmotivated. Why? Because most online discussions are nonfictional, and women tend to insert themselves into nonfiction writing more often due to their "relational" writing style. Since men tend to be more "informational" this behavior may strike them as jarring and deliberate rather than a natural extension of the way that women normally speak. The concept of "mansplaining" is likely based on a similar misunderstanding of gendered differences in communication, but that's a story for another day.
tl;dr - Men talk about facts and objects, women talk about relationships and people. These aren't just subjective stereotypes, they're backed by objective data.
