It's not entirely ahistorical, because the situation in House of the Dragon is based on the actual EARLY medieval situation of Empress Matilda (1102-1167), the daughter of Henry I of England. I have a previous answer relating to this which I'll quote below:

Technically, there was a ruling queen prior to Mary I. The only previous time in English history that a woman attempted to rule in her own right as her father's natural heir was Empress Matilda (1102-1167), the daughter of Henry I and granddaughter of William the Conqueror; at this time, it hadn't even been fully established that princesses could pass inheritance rights on to their sons, so it's remarkable that Henry decided to make her his heir in the absence of other legitimate children of his own. The following summary of the situation may sound familiar to you if you read or watched The Pillars of the Earth. When Henry I died in 1135, his nephew, Stephen of Blois, was able to get crowned in London since Matilda, married to the count of Anjou, wasn't able to make the journey immediately - the idea of the heir immediately becoming ruler on their predecessor's death wasn't yet a tradition. In 1139, she did travel to England, though, and sought out the support of local barons to wage a military campaign against Stephen. She prevailed and ruled for a short time in 1141 but didn't make it to a coronation before being dethroned, and kept on being "Lady of the English" until her half-brother and chief supporter, Robert of Gloucester, died in 1147. She then left for France, giving up on her own personal claim to the English throne.

In the very small number of primary sources left about Matilda's short reign and longer campaign, there's a lot of discussion of her gender. Without any precedent for a woman ruling England (though Anglo-Saxon queens had been able to wield their own kind of power as kings' wives or mothers), she had to construct a version of female kingship that led to her taking on a lot of masculine features. Henry had had her take the same normally-masculine oaths her late brother had made as heir, and while her gaining this position required her to remarry far beneath herself in order to produce her own male heirs, instead of taking on that new title she was considered largely as her father's daughter and an empress (her first husband had been the Holy Roman Emperor) and held onto most of her dowry. Once she began her quest for the crown against Stephen, she threw off conventions of gendered behavior and acted quite openly in her own interest: she captured opponents and held them in chains, legally appealed Stephen's succession, and, well, acted as a king among her own vassals.

Although there hadn't been any explicit opposition to her claim just on the basis of her gender, opponents did use her status as e.g. the wife of the Count of Anjou as tools to delegitimize her standing. Once she had some power, though, her lack of feminine reticence and modesty became a problem even in the chronicles that otherwise supported her. It wasn't so much an issue that people said, "hey, women shouldn't rule," but that once a woman was actively exercising power on her own behalf without cloaking that in concern for her son(s) or a pretense of not wanting to do it. Most kings had queens to project softer, interceding, and more forgiving royal power by their sides, rounding off their corners while they were able to make the hard choices and do nasty, bloody things. Matilda simply didn't have the advantage of this kind of partnership, and couldn't be both the king and queen.

So, Mary. While in general Matilda is not considered a proper queen regnant because she was never crowned (let's note that nobody has this problem when it comes to Edward V, one of the princes in the Tower, just saying), there is no doubt that Mary I ruled officially. Matilda was her only pattern when it came to English queenship, and due to the above, she was more valuable as an example of what not to do - despite the centuries between them, it would still not have gone over well if Mary had flouted what was expected of a woman and simply behaved like her father as a monarch.

Mary's Catholicism was a much bigger issue than her gender as a fact on its own, in a kingdom that had recently switched to Protestantism as the state religion, with a government full of people who'd fully bought into it. Where her gender came into it was the concern about where her husband - someone she was regarded as needing in order to produce her own heirs to keep feuding cousins from starting another civil war - would stand in relationship to the throne. Married women were considered femes couverts in English law, subsumed into their husbands' legal identities, which implied that a queen's husband perhaps might automatically be in charge of the country. Edward VI's "Device for the Succession" (which outlined who would follow him to the throne, since he had no heirs) excluded both Mary and the Protestant Elizabeth out of concerns about their marrying foreign princes - as would be appropriate to their station, being born princesses, even if they'd been later declared bastards - and subjecting England to foreign rule, diverting the line instead to Jane Grey, already married to an Englishman, "and her heirs male". (Jane was, technically, of course, another precedent for Mary. She planned to make her husband a duke, rather than allowing him authority over herself.)

Once she'd declared herself the queen, Mary quickly attracted support from the local gentry and nobility despite her gender: she didn't have a husband ruling over her yet and was also no longer a ward of any man, and therefore feme sole, a totally independent woman. While Mary did have to start off with a bit of military violence, unlike Matilda she had no real challengers and was therefore able to drop the masculine-coded aggression in defending her right to rule, inhabiting the office of kingship as a "normal" woman without really upsetting the overall patriarchal power structure. (It was also enshrined in law by this point that daughters could inherit from their fathers and brothers, so it simply made logical sense to most people that she was now the monarch.) She went to her coronation in cloth of gold and with her hair down, as in the famous coronation portrait of Elizabeth I, the traditional way for a king's wife being crowned to appear, and later billed this ceremony as her marriage to the realm, a marriage in which she was obviously the bride. In general, she modeled herself on her pious mother, Catherine of Aragon, rather than her powerful and somewhat arbitrary father - typically, this is presented in pop culture as just a part of her fanaticism, rather than the use of a traditional aspect of queen-consortship. She was publicly rather submissive to her advisors and ambassadors, confirming her status as an unmarried woman above her status as monarch and allowing them to believe that she was naive and trusting, as they expected her to be due to her gender. Before she wed Philip II of Spain, she talked up her desire to remain chaste and made it clear that her main reason for marriage was the succession (the ensuring of which would make her pregnant and therefore extra-womanly); she allowed it to appear that she was totally uninvolved with the negotiation process for his hand, as though the men were deciding her fate. (Despite all of this, she made it clear in her marriage paperwork that she would continue to be the ultimate authority, reducing him to the traditional female role of intercessor and soft-power-holder, and that Philip's title of "king" was only a courtesy, and she also brought no dowry at all to the match - far from the expected behavior of a royal bride, in general!) Rather than bringing herself into the masculine role of king, basically, she brought the role of kingship to herself while staying firmly in the female sphere, and while her sister's reign was longer and more successful, it's clear that Elizabeth took a certain amount of direction from the way Mary handled her gender.

Both of the two "first" queens regnant of England had a great deal of trouble in ruling (and in later biographies) as a result of the way that others perceived their gender and their ability to conform to its conventions. Their problem was the social practices surrounding their gender, that is - not just their gender in and of itself. It's difficult to get into the historical mindset that saw women considered the property of their male relatives throughout their lives (unless they were lucky enough to become rich widows) and yet also considered women not biologically unfit to rule a country. In part, this difficulty is supported by hundreds of pop cultural depictions of historical men as total chauvinists who thought women were simply stupid across the board, which ignores the reality that elite women did a lot of work in estate management and diplomacy, and which they recognized as valuable. It's a contradiction. People have a lot of contradictions, even today - we don't run on pure logic, although many think they do and use that to prop up their own internal contradictions.

You might be interested in reading The Lioness Roared: The Problems of Female Rule in English History, by Charles Beem (2006), which is 100% about this issue and was my major source for this answer. It's great!