Computer role-playing games. This trope is true in many of them simply because female gamers play these games too. Usually, this trope is handwaved and never commented upon. In older RPGs, however, it was common for there to be gender-based stat adjustments, usually with male characters getting a bonus to strength and female characters getting a compensating bonus to charisma, dexterity, or intelligence.
Specific games:
The futuristic militaries in Call of Duty: Black Ops III are this. The advent of cybernetic augmentations has rendered physical differences between men and women non-existent, and since the focus of warfare has shifted from aerial and technological supremacy back to foot soldiers, anyone capable of fighting is in high demand. Notably, not only are the titular black ops squads gender-integrated - and the Player Character can be male or female - but the enemies the protagonist is pitted against are male and female as well, averting the Men Are the Expendable Gender trope. Notably, though only enemy troops are egalitarian. Friendly generic soldiers are always male.
Age of Empires III had female characters who fully acted as combatants, which was never mentioned by anyone in-game.
Ranges from being downplayed to being played straight depending on the specific game, but it is always present. The early games in the series have purely male generic guards, soldiers, bandits, etc. but named characters in these roles can be of either gender. Later games in the series introduced more women in these roles. It seems that in Tamriel, there's nothing stopping women from signing up, but they just don't join up as often. The deep backstory is also chock full of notable female monarchs, faction leaders, and great heroes.
After being a One-Gender Race of all male lesser Daedra in Oblivion, Online introduces female Xivilai. Both genders have similar combat prowess, spellcasting abilities, and status.
Reveals this to be the case for Skyrim's Jarls (Earls). Jarls can be either men or women, and their children inherit their title regardless of gender. When characters debate who the next High King of Skyrim should be, disagreements have more to do with philosophy and allegiance than the gender of the candidate, and no one questions Elisif's claim to the crown because she's a woman.
Historically, Skyrim has also had many badass warriors of both genders and several legendary figures in Nord are women.
Female soldiers are rare, but still present in the game though mostly on the Stormcloak side, while the Imperial Legion has Legate Rikke as its most prominent female member. There are also plenty of female bandits and Forsworn.
The Fallout universe has a fairly equal amount of female and male bandits, raiders, quest-givers, and such. Justified in post-apocalyptic settings, really, since it would be stupid for society to waste any able pair of hands.
Until Fallout: New Vegas introduced Caesar's Legion. The Legion represents conservative values taken to their logical conclusion (i.e. emulating the past), and not only do characters comment on what a bad idea this is, but the Legion also alienates a large amount of the population as a result.
As a counterpoint, the NCR is highly egalitarian when it comes to gender. Women can be found in every role within the NCR's society and military, which makes sense since probably the most influential figure in their history has been Tandi, who was female and eventually became President. And even with the more chauvinist policies under President Kimball's administration, women can still rise up the ranks with distinction; compared to the Legion, the sexism that's crept into the NCR is outright benign.
Final Fantasy Tactics has no gender disparity in their army units. Class, however...
The many soldiers serving their city-states in Final Fantasy XIV have a near equal amount of males and females fighting alongside each other. Subverted with the Garlean Empire where the common foot soldier are males while the females serve in higher ranks like Commander and are rarely seen.
Fire Emblem mixes the genders readily, both in the army as a whole and within the different classes. Only a handful of classes are single-gender, including the all-women Pegasus Knight class. This got played straighter as of the Fates installments. All classes became available to all gender, with their names being changed. However, Pegasus Knight and Valkyrie, otherwise female only, became Sky Knight and Strategist. Similarly, the otherwise male-only Fighter class became accessible to female thanks to Charlotte, and the Hoshidan equivalent to it (Oni Savage) had Rinkha as its representative. However, there are some special DLC-exclusive classes such as Witch, Starlode, and Bride that are available only to a certain gender. The Dancer class is also only accessible by Azura.
The first two games and the novelizations subvert this. Only men do the fighting. All fertile women are used for reproductive purposes, while non-fertile women serve in support roles. The third game, however, plays this straight. The women fight alongside the men. This is because humanity is down to its last throes and needs every available body to fight.
Before Emergence Day active female Gears were not unheard of and were at least as common as female soldiers are today, some examples introduced in the Aspho Fields novel being Bernadette Mataki and Helena Stroud, Stroud being the commander of her own company and the mother of Anya from the games. Gender equality and civil rights took a nosedive after most of humanity was killed after E-Day and men became more expendable than women.
The franchise seems to be gender-blind when it comes to humans, for the most part. Possibly quarians as well, considering the only quarian military groups we ever see are led by Tali and the Admiralty board splits 60/40. Other alien races don't show their females at all (the asari, being a One-Gender Race, don't count), but Garrus' war stories show that the turians are integrated too. Restrooms are still segregated, though, as EDI will remind you if you stumble into the wrong room. Maybe a Justified Trope with genetic enhancements being standard for soldiers of humanity.
Salarians do not follow this rule though since their species breeds too few females to throw them into combat. Instead, they're actually a matriarchy where the few salarian females are always given positions of leadership and authority.
Tali and Ashley discuss this in the first game. Ashley mentions how long it took human women to prove they could handle shotguns, with Tali replying that the Flotilla can't afford the "luxury of sexism".
In Lair of the Shadow Broker, one of the files states that infertile krogan females at least have garrison roles on their homeworld. All krogan are taught how to fight from childhood, it's a question of who they can afford to risk. Indeed, stories of krogan history prior to the genophage suggest that krogan females had equal rights and were just as respected as the males (the female Warlord Shiagur is often mentioned as being one of the most legendary badasses the krogan have ever known). The only reason krogan females are kept cloistered away in modern times is because the genophage has forced the krogan to safeguard their females to ensure the survival of their species. Clan Nakmor in Mass Effect: Andromeda (which has mostly overcome this problem) plays the trope straight: the clan itself is led by the female Nakmor Morda, while Nakmor Kesh is Superintendent of the Nexus.
Interestingly enough, the first game plays with this trope a bit in terms of your options of NPC allies: classes that specialize in one form of warfare (Soldier, Adept, Engineer) are given to female characters (Ashley, Liara, and Tali, respectively). On the other hand, hybrid classes (Vanguard, Sentinel, and Infiltrator) are provided by males (Kaidan, Wrex, and Garrus). However, the Player Character, Shepard, can choose to follow this trend or avert it, based on their gender and class selection.
Dragon Age mostly portrays Thedas as being egalitarian when it comes to gender:
In the vast majority of nations and cultures women are allowed to serve alongside men in the military and become knights and other warriors such as templars and Seekers. The Grey Wardens are mentioned as having fewer female members than other martial orders, likely because women are made into broodmothers by the darkspawn, but this seems to have been Retconned in later installments. Heir Club for Men is apparently nonexistent in the nobility and royalty, with the eldest offspring being the heir regardless of gender. Women can also be scholars, politicians, and leaders in the Circle of Magi without any protest. Justified as the setting's equivalent of Jesus Christ was a woman, and her status as a role model explains why a society that falls prey to many of the same social ills that plagued real-life medieval Europe is so gender-egalitarian.
Krem mentions in Dragon Age: Inquisition that in Tevinter's military women are allowed to fight but are segregated from the men, but otherwise there is no indication that the Imperium is different than the rest of Thedas, aside from their Chantry (see below).
The Qunari come the closest to having a Stay in the Kitchen attitude, albeit towards both genders, as they view men and women as equally worthy and important but having innately different roles in their society. Those who transgress against these gender roles aren't punished for their nonconformity but are declared effectively transgender and treated as the gender that matches with their new role.
The Chantry, the main human religion, actually is segregated. Although lower positions have a few men mixed in, all priests and higher administrative positions are required to be women. This is flipped in Tevinter, where all higher-ranking officials are men. According to Dorian, they did this basically to spite the southern Chantry and separate themselves from them.
World of Warcraft players abide by this trope, but the societies they're theoretically members of aren't necessarily so accepting. Most notably night elf warriors are female and druids are male.
The night elves are one of the few notable exceptions. For the vast majority of WoW's cultures, this trope is played completely straight.
It's mentioned that due to the casualties suffered during the war against the Legion in Warcraft III, the night elves have dropped their traditional gender requirements. (Also, they were only requirements for joining the Sentinels or formal druidic training, respectively - there's no rule that says a night elven man couldn't be a badass swordsman on his own.)
Dwarf Fortress plays it straight for most humanoid species; the game's code could grant bonuses or even make certain skills exclusive to one gender or the other, but currently doesn't.
Arcanum: Of Steamworks & Magick Obscura imparts a strength penalty and endurance bonus on females (which can be negated by taking the "Tomboy" background) but otherwise does not question the idea of a female magician, a female inventor, a female warrior, or a female sailor, nor does anyone complain about a female adventurer wandering the countryside with five men or delving into ruins and caves. Virgil will comment on the oddity of (male elf) Nasrudin reincarnating as a woman but has no problem with it otherwise. The times you're directly treated differently due to your gender can be counted on a factory worker's right hand.
In Bioshock Infinite, despite the fact that Columbia has some seriously regressive social values, gender doesn't seem to be a problem as you can clearly see women fighting for both the Founders and the Vox Populi (the latter even being lead by a woman). It's even the cause of some Enemy Chatter when one Founder is shocked at the inequality down in early 20th century America. Making it all the more shocking that they don't blink an eye at some horrific racism.Fridge Brilliance when you think about it. Comstock would want to remove sexism from Columbian society since he was grooming Elizabeth to replace him as Columbia's leader.
Xenonauts: Let's face it, having so many female military officers in 1979 is a bit of a stretch.
In Long Live the Queen, the kingdom of Nova operates on absolute primogeniture: the eldest child, male or female, inherits their parent's title.
In Detroit: Become Human, the U.S. soldiers that raid the Android rebellion's stronghold include female units, three of whom can be directly killed by the main characters.
Despite being set in fantasy-World War II, the Valkyria Chronicles series has a rather equal gender divide for both Gallia and the greater Federation, although Empire troops tend to be all male. The games do explain it, though: Gallia has a policy of Universal Conscription and everyone receives military training in high school, so when the militia is activated the women are called to arms as well. The Federation allows anyone to enlist, and everyone who wants to fight on the front lines goes through the same basic training; male or female, if you pass, you can serve. The Empire practices more traditional conscription, dragging any able-bodied young men to the frontlines as necessary but sparing the women to run their factories.
In The Sims, female Sims can do anything male Sims can. The only exception to this is using urinals and even that could probably be changed with a mod or cheat. Male Sims, meanwhile can bear children just like female Sims if the right cheat code is used.
In Rimworld, every faction uses both men and women as soldiers. Also, backstories of characters sometimes indicate they were members of the military, and you can find women who were space marines or mercenaries as much as men.
Muv-Luv: the franchise has plenty of women in the military... in fact, women outnumber men in the military. The explanation for this is that initial battles against the BETA went so catastrophically poorly and losses were so high that there simply aren't enough young men to recruit for the military anymore.
Saints Row has done this throughout the series, with the second game featuring just as many male cops as female cops, as well as an equal amount of male gang members and female gang members, resulting in a rather very diverse cast for a gritty crime game.
Metal Gear Solid 3: Snake Eater: For a game set in The '60s, very few people make a huff over the fact that The Boss, one of the most notable soldiers alive, is a woman. It's implied that nobody ever dared to bring it up because of her connection to the Philosophers and because she is just that good.
EA's Super Mega Baseball franchise has co-ed teams in a sport that's traditionally all-male, and even has its own Distaff Counterpart in softball.note Though many adult males play softball recreationally in co-ed leagues, while females playing baseball anywhere but the earliest youth levels is pretty rare. Gender has no effect on player ratings, the female players can throw just as hard and swing the bat just as well as the male players.
and Helena Stroud