Unisex Series, Gendered Merchandise

Sokka: There's no girls in the Avatar universe.
Aang: There's not?
Sokka: Of course not. Just ask Mattel.

— Avatar: The Last Puppet Bender - Hot Air

Merchandise is a tricky thing. Often times, merchandise producers don't seem to take note of what the work is about. A lot of merchandise will blatantly go against a work's morals or feature the characters doing things they'd never do. Merchandise also has a tendency to be aimed at one gender that isn't the entirety of the audience. A work with a unisex audience will end up with merchandise aimed at either mostly men or mostly women.

Children's works are especially prone to this. Gender neutral toys exist, but in general, toys are broken into "boy toys" and "girl toys". This leaves unisex works in the middle area, forcing them to appeal to only one gender. The protagonists are mostly boys? Make a bunch of boy toys. Mostly girls? Only make girl toys.

This often results in a work falling into the Girl-Show Ghetto. Female characters will rarely get any promotion if the merchandise is aimed at boys, no matter how much of the main cast is made up of girls; likewise, any work with merchandise aimed at girls will either ignore or heavily downplay the existence of its male cast. Gendered merchandising can actually affect the work's longevity (especially works that become popular with a completely different demographic than intended). The demographic of a work failing to match the heavily gendered marketing has resulted in works being prematurely canceled.

Examples:

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Anime & Manga

Although it wasn't aimed at a specific gender, the merchandise for Osomatsu-san is almost exclusively marketed towards young women.
Zig-Zagged with Digimon. Unlike many examples, a few of the female characters did get toys, but only the androgynous or masculine looking ones like Garudamon or Taomon got any of the good ones (and even then, the toy commercials would only show the male Digimon), with the more overly girly Digimon like Lillymon and Angewomon only getting cheap crappy toys, if any at all. With the exception of Pocket Culumon, none of the commercials ever showed girls playing with any of the toys. Kari was also the only 02 character not to get a Digivice toy, for the crime of... being the color pink. Starting with Digimon Adventure tri. this was averted, as the marketing became gender neutral and the female characters finally got more merch.

Films — Animation

Disney Animated Canon films are aimed at a general audience. Their merchandise? Not so much. While gender neutral Disney merchandise exists, a good chunk of it is aimed at female audiences (especially little girls). This reached its peak when the Disney Princess line was created. Almost all Disney films starring royalty (even Aladdin, where Jasmine is a secondary character) get pinned under the line and end up with mostly girl-aimed merchandise.
Pixar merchandise is mostly aimed to boys, even when their audiences include both boys and girls equally. Some notable examples are Cars and Toy Story series, whose toys are aimed at boys only. Brave' is an exception, with Merida being lumped in with the Disney Princesses despite not being part of the Disney canon.

Films — Live Action

The Force Awakens: Despite the lead character being female, merchandising for the movie completely ignored her existence and focused on the male characters. This led to the popular #WheresRey hashtag, and to calls to boycott licensed toys unless the toy line included a Rey figure.
There was a backlash when the toys based on the family-targeted films The Avengers (2012) and Avengers: Age of Ultron were released because there was no action figure for Black Widow (the only female member of the team). Notably, in the latter film, she rides a motorcycle and uses Captain America's shield in conjunction with it, but all the toys had Cap riding the bike himself.

Super Mario Bros. is a gender-neutral franchise, but a large amount of Mario merchandise gets put in the "boy's" aisle, Princess Peach merchandise being the exception. This was a reason given for making Tetris a pack-in game for the original Game Boy over Super Mario Land, since Nintendo didn't want the console to be viewed as exclusively a "boy's toy."
Similar to the Super Mario Bros. example above, Sonic the Hedgehog is aimed at both genders and includes a cast of female characters (Amy Rose is obvious). Half of the merchandising is marketed with and to young boys, probably because a blue hedgehog with an attitude and robots fit in the "boy's" section. The female characters are more likely to appear in the gender-neutral merchandise, most are to appeal to the adult Periphery Demographic.
Splatoon:
- Of the three manga made for the series, the two shonen series (Sankichi Hinodeya's manga and Ikasu Kids 4-koma Fest) promote the male inklings over the female ones despite having Gender Equal Ensembles: Team Blue is split down the middle but is led by the male Goggles, while Hitto is typically accompanied by Maika. The only one that doesn't follow this pattern, fittingly, is the Honobono Squids manga that runs in the general-audience Weekly Famitsu.
- For a unisex series that uses the female inklings as the default and has very prominent female NPCs, this is surprisingly averted with the non-manga merchandise. The heavy focus on unisex fashion and music in the game might be behind it.
Zig-zagged with Pokémon:
- On one side, most of the manga are predominantly aimed at boys. Pokémon Adventures is considered kodomomuke but it is rather shonen-leaning. There's only been one shoujo manga. The anime on the other hand is firmly kodomo, with elements that appeal to both female and male fans.
- Game merchandise tends to be gender neutral. There is also plenty of merchandise aimed at boys and girls, of different ages.
Atelier is for a gender neutral audience, and most games have a Gender-Equal Ensemble or even a Cast Full of Pretty Boys. In fact, a survey revealed most players are women. Despite this, most of The Merch seems targeted towards a male demographic, with things like scantily-clad figures and fanservicey art prints that make the series look more like a Bishojo Series.
Starting in The New '10s, most of The Merch for the gender-neutral Tales Series became more geared towards women, consisting mainly of bishonen goods.
Kirby remains gender-neutral even with its Sugar Bowl aesthetic, though most of its merch skews towards older women with goods like accessories, makeup and plush toys.
Mega Man (Classic) is a gender-neutral series, but—possibly because the main character is a blue robot—almost all merchandise for it ends up in the boys' section (merchandise featuring Roll being an exception). The same holds true for any animated adaptations that use the classic series as a base, like the 1990s series and Mega Man: Fully Charged, as well as later spinoffs like Mega Man X and Mega Man Battle Network.
In Japan, Yo-Kai Watch is a unisex franchise. In America, however, marketing treats it as a "boy's series". Most clothes, even adult-aimed ones, are aimed at males. The original female protagonist, Katie, is barely advertised (including Nate being on the front cover of Yo-kai Watch but not Katie, unlike the Japanese cover which didn't feature humans) and her Yo-Kai Watch has never been exported outside of Japan. Even a shoujo manga starring Katie was never translated, while the more unisex manga starring Nate was.

Western Animation

Word of God is that The Powerpuff Girls was a gender-neutral cartoon. However, as the protagonists were cute little girls in bright colours, almost all merchandise was aimed at girls. This was taken to its natural extreme with both the Magical Girl adaptation called Demashita! Powerpuff Girls Z and the 2016 reboot being explicitly aimed at girls.
Zigzagged with DC Comics adaptations. On the surface, the shows look gender neutral. However, they are Merchandise-Driven, and all of the toys are aimed at boys. DC has not taken kindly to the female Periphery Demographic in the past and caused shows such as Young Justice to be cancelled due to not selling enough toys to boys. They have, however, made works aimed at girls such as DC Super Hero Girls.
Modern day Betty Boop merchandise is almost always aimed at women. This is despite the original shorts being gender neutral and, if anything, Betty was Ms. Fanservice eye-candy aimed at men.
Dora the Explorer is a gender-neutral cartoon meant to teach kids Spanish (or, in some dubs, English). Despite this, most merchandise is aimed exclusively at girls. This came to the point where Go, Diego, Go! was created as a Spear Counterpart (despite being equally gender-neutral) and the sequel spinoff was aimed only at girls (with The One Guy Pablo), complete with Dora getting a Girliness Upgrade. Oddly enough, the merchandise started off unisex, but after a few years it began being aimed at only girls.
PAW Patrol is a preschool cartoon about dogs (and it even has two female puppies on the team), but most merchandise is aimed at boys, with some pieces of merchandise even omitting Skye and Everest. The exception to this is merchandise featuring just Skye and Everest (the two female members) and the occasional male character (usually Marshall), which is geared towards girls.
In terms of marketing and merchandise, The Lion Guard is treated as a Spear Counterpart to Sofia the First. This is despite it being an unisex Edutainment Show based off an equally unisex Disney series.
Infamously, Avatar: The Last Airbender toys excluded the female characters, especially Katara, which might explain why they stopped making them by the end of the first season. Its female-lead sequel series The Legend of Korra outright didn't have toys.
Legion of Super-Heroes had prominent female members and a fanbase of boys and girls. Toys however, were aimed entirely at boys. The cartoon attempted to change the unisex fanbase by drastically reducing the screentime given to female team members, but it was eventually cancelled after its second season.