It's important to contextualize the claim: this doesn't actually happen in an overwhelming number of historical movies and tv shows. It tends to mostly happen in a specific subgenre that focuses on male leads and male supporting characters who are rugged and usually unkempt, and centers on battle scenes and shows of physical or institutional political power. These plotlines typically have little to no space for "feminine" female characters except in a few stereotypical minor roles, requiring female characters who are to spend more time onscreen to take part in battle scenes and the like. I'm not going to argue whether or not feminism can be considered a "trendy ideology" here, but I'd point out that female warriors are very popular with the public for a number of reasons - there are people who relate to them, there are people who get aesthetic pleasure from them, and there are people who are attracted to them - and that writers, directors, and studio execs may very well press for their inclusion in order to cash in on the popularity of the type, or to cast a particular actress in an important role, or for their own personal preferences. They may also simply accept them as a common stock type and include them by default.

When it comes to the question of the accuracy of these portrayals, things get a lot more complicated. It would be nice if issues as murky as gender roles could be identified as "accurate" or "inaccurate", but the best you will generally get is "the average woman wouldn't, but ..." Despite persistent beliefs about women as a class, the historical record is dotted with exceptions and inconsistencies.

I want to start by noting that the coronation scene in Outlaw King (which I think is what you're referring to, as Hal is crowned in The King by an older male priest) is actually true to the historical record: Robert the Bruce was crowned during his coronation ceremony by Isabella Comyn, Countess of Buchan and daughter of the late Duncan MacDuff, Earl of Fife. There was a somewhat mythical tradition that Malcolm III had given the MacDuff family the right to crown Scottish kings as a result of Lord MacDuff's assistance in bringing him to power - certainly not something that continuously existed from the eleventh century on, but it could be very symbolically powerful. Symbolic power is important to all monarchs, but it's particularly vital when a monarchy needs to assert itself as legitimate against opposition - such as Edward I and his claim to authority over Scotland. Isabella's brother, Duncan, would have been the natural person to do the coronation, but he had been captured by the English at this point and wasn't available; as a result, Isabella had to sneak out and take the role in the ceremony herself to give it legitimacy. (She had to sneak because her husband was an enemy of Robert the Bruce. That she could and would do this despite that fact should help to put her agency and importance as a person in context.) This is a pretty good warning not to assume that women had no place in political events and that their inclusion must mean that a writer is "faking history".

Female viking warriors like those in Vikings and The Last Kingdom are less clear-cut. Medieval Icelandic laws put penalties on women who wore men's clothing (and vice versa), cut their hair short, or carried weapons, and the fictional Laxdæla Saga bears out that this was indeed a taboo. However, just as medieval Scots could conceive of women having political uses outside of marriage when it suited them, vikings could imagine women with weapons - armed and armored valkyries seem to have been a widespread concept in their culture, and the post-Viking-era historian Saxo Grammaticus wrote about a number of warrior women drawn from earlier literature. It's also important to note here that Saxo specifically wrote about Lagertha, wife of Ragnar Loðbrok (two of the main characters of Vikings), as one of these warrior women. Despite the fact that neither valkyries nor these warrior women likely existed, the parallel fact that they were part of Viking "pop culture" is relevant. (There has been a discovery within the last few years that a grave on the island of Björkö in Sweden, which is otherwise exactly what would be expected of a high-status warrior, contains a female skeleton; the interpretation of this grave is still somewhat up in the air.)

But now that we have your examples out of the way, I think we need to discuss "faking history" more broadly. Because the fact is that these shows and movies you're talking about are riddled with issues. To name a few, but certainly not all:

• The King puts off the blame for Henry V's clashes with the French onto a courtier, William Gascoigne, when in actuality Henry Chose to continue the Hundred Years' War in order to pursue his and his family's dynastic claims to France

• The same movie also gives Hal a friend in Falstaff, a fictional character created by Shakespeare who did not exist in real life

• There is no evidence that vikings were tattooed as they are in Vikings (see this answer by /u/platypuskeeper)

• Ragnar and Lagertha are essentially figures from folklore and may not have ever existed, while Rollo was definitely a real figure and therefore probably not related to Ragnar

• Christians of the period of Vikings would not have tortured/killed an ex-monk they viewed as an apostate, let alone by crucifixion

• There is no evidence that Uhtred the Bold was stolen in childhood by vikings, or that such a child could grow up and simply come back to England. The Last Kingdom also invented Aethelflaed's kidnapping, and Aethelraed's personality - there's no evidence of them, either

• Outlaw King is significantly more accurate than, say, Braveheart, but it still problematically makes Robert the Bruce seem to be driven by a love of the Scottish people rather than personal ambition

Making kings like Robert the Bruce or Henry V into gentler souls who just want what's best for their people and would ultimately prefer not to fight is done to appeal to modern mores, and in general medieval-set fiction tones down the level of Christian piety that would be accurate for the same reason, with most characters relatively indifferent to religion and actual priests often made to be hypocrites. The level of importance and agency that royal and aristocratic women could have is nearly always understated, from the level of estate administration that they were expected to handle to their personal roles as diplomats and ambassadors.

If people take historical dramas as truthful - and I know they do, based on popular ideas about women's clothing in the past few hundred years - then there is no reason for female characters having anachronistically masculine roles to stand out above any of these issues.

Actual vikings didn't have tattoos either. They probably didn't perform 'blood eagles'. Ragnar Lodbrok isn't considered to have existed in the first place, certainly not in any form that resembles the sagas (which isn't even possible given they're contradictory).

There is no reason to assume the 'Ragnar' the looted Paris had anything to do with him. The siege was also in 845, which is more than 50 years after the raid on Lindisfarne, which Ragnar supposedly also took part in, in the show.

No Norseman was ever executed in a snake pit. It's a saga trope that's absurd; there aren't even any deadly snake species in northern Europe. Not that it's depicted in the show with European snakes but rather harmless Ball Pythons (west-central Africa), Boa constrictors (South America) and I believe I saw a North American Corn Snake or two in there. Production-wise it's of course sensible to use docile pet snakes in addition to the vicious CGI ones.

Uppsala temple was not on a mountain in a forest, it's in the middle of a cultivated flat plain. More generally the show's Scandinavia looks a lot like the Norwegian fjords, when in reality Denmark is extremely flat and so are the regions of Sweden that were most important during the Viking Age. They live in a place named "Kattegat", that looks like it's deep in a Norwegian fjord, nestled between steep mountains. But the Kattegat that actually exists is the strait between the Danish peninsula of Jutland and the coast of Halland in Sweden. It's flat and sandy and looks nothing like the fjords of Norway. "Kattegat" also not an Old Norse or Scandinavian name; It's a Dutch name from the 17th century. In other words, that's as accurate as having Native Americans of the Lenape tribe saying they live in "Brooklyn", 700 years before Columbus. ("Brooklyn" being another name of 17th century Dutch origins) Oh, and their "Brooklyn" also looks like Texas; full of mesas, desert and saguaro cacti because the producers thought that's a 'more American'-looking landscape than where they actually lived.

That's not even getting into how the depictions of pagan cult are more or less entirely invented from scratch. Vikings didn't use the "végvisir" and other symbols culled from 19th century, which didn't even originate in Scandinavia.

I could've absolutely have gone on longer; my list of inaccuracies is limited only by the fact that I've not seen a single complete episode of the show, just some clips and parts.

The TV show 'Vikings' is not historically accurate at all. Where it is based on anything it's based on sagas that are not in themselves considered trustworthy historical sources; they're recorded 4-500 years after the events they're purporting to describe here.

The sagas have shield-maidens. They have women who fight and kill. They even have a woman who became king (not queen, she insisted) and dressed like a man. Female warriors as part of Norse folklore are fact. Whether female warriors fought in battle is unknown. Weapons grave finds do indicate women do seem to have been able to have the social status afforded a warrior. It is a topic of active debate in academia.

That makes it not-incorrect-at-all if we're going to judge it on faithfulness to the Sagas; which rather absurd things like snake pits perhaps indicate we should. By the stricter standard of known reality, it's as said 'debatable'. But even 'debatable' status makes it already much more accurate than a myriad of things that are completely made up and not based in reality nor saga, and a myriad of other things known to be false. So why does this particular inaccuracy strike you as so grievously wrong?

I understand that there is a current trendy ideology along these lines,

Yes, currently there's a lot of people that acknowledge that women have for a long time been under-represented in film and television in general, and especially women doing things that go against traditional (for our society) gender norms. So?

It is not "faking history" to therefore emphasize stories about women or the roles of women in historical stories. It's just a new take on the same material. (it's also good business sense, considering women watch about as much TV as men do)

If you think previous depictions were not rooted in the ideologies and biases of their own times, you're delusional. The very notion of "vikings" (as if they were a people) and fascination with them is entirely due to the political biases and programs of the early 19th century romantics and nationalists. It was they who plucked 'vikings' from having been an obscure term known only to Scandinavian historians and turned it into a cultural trope. They invented the horned helmets and for all intents and purposes the 'viking' image. From writer Sir Walter Scott to the visual artist William Morris, they idealized them, they projected their own values onto them, and they emphasized whatever parts they liked. For instance, the English professor George Dasent, translator of Njal's Saga, had this to say about the vikings in the 1870s:

“They were like England in the nineteenth century: fifty years before all the rest of the world with her manufactories, and firms and five and twenty before them with her railways. They were foremost in the race of civilisation and progress; well started before all the rest had thought of running. No wonder, then, that both won.”

They didn't refrain from using horned helmets in Vikings because it was historically wrong, they removed them because it was passé, too old-fashioned-viking-trope. Too "Hagar the Horrible". They gave them tattoos instead. Which doesn't have much more historical basis either, but does on the other hand fit better in with today's conception of what's 'tribal' and 'barbaric'. More generally you have that emphasizing of the 'barbaric' here, of preferring to show uncensored violence where Victorians would rather emphasize things like loyalty and virtue. Again that's a choice rooted in contemporary values. Violent antiheroes sell better than morality tales.

The whole pop-cultural 'viking' concept has since its inception been heavily burdened with the biases of the time in which it was created. The fact that you accept these without question and ignore far more grievous inaccuracies, while pointing to contemporary biases, is hard to see as much more than a statement to the effect that you prefer certain older biases.

Though not focusing exclusively on the issue of gender, this older Monday Methods thread on how we perceive accuracy and authenticity in popular culture may go some way towards offering a historical viewpoint on such portrayals.