Maybe this Will Put Things into Perspective about Rhaenyra & Cersei's Kids Being Bastards or Not...
Feudalism is an early period or a economic phase of a millennia-managed con against anyone who isn't a noble man, and most men are the active conmen.
Neither set of kids were ever declared bastards. Nor were they ever or "acknowledged" as bastards, because noblemen "acknowledge" a child they father onto another woman. noblewomen, in theory, can, but if their having had sex premaritally/extramaritally isn't already known outside of the household they do not. Because to do without it already being known (like with Alys Turnberry) would publicly ruin her prospects for marriage in the future, ruin her reputation, and likely muddy the family's as well.
Robert probably would have removed those kids from the line of succession had he known (and he didn't) if not outight remove them from the mortal coil. But instead, he got gutted. Therefore, Cersei's kids are not officially or "legally" bastards. That prior declaration is what is required to have them "legally" known as bastards.
Bastardry has always been more of a legal question in its nature than a biological fact of nature. Of course, we the audience and most of ther know that Rhaenyra's kids aren't Laenor's biologically; Ned correctly deduced that Cersei's weren't Robert's biologically. However, he was never able to get his information to matter "legally", or to get it to Robert to make a decision on. Whereas Laenor, Corlys, Viserys all knew and decided to maintain the boys as their heirs. And they made this decision based on the lack of knowledge the public has/what they can control. Which is often what any noble does; once again, GRRM has explicitly stated that the lords of Westeros often take advantage to twist "laws" (customs) according to the circumstances around them & their own desires, and it's is not exclusive to bastards already "acknowledged".
The purpose of marriage as an institution is entirely for the lord/nobleman's benefit. It is an institution that was created and developed entirely for a man's political interests (a father's, a brother's, a husband's, a son's, etc.). And it was made to consolidate/monopolize the noble woman's (or really any woman) body and reproductive labor so as to produce living products to pass on the resources/titles mainly the lord and his ancestors have aggregated. To try to make sure those resources are passed to the people the lord wants passed own to, the sexual purity culture imposed on women and girls works to construct shame & suppress female extramarital and premarital sexual activity, which is an aspect of her overall agency. Her agency is re-confined/socially reduced to her sexual activity because she has no other primary function nor legal privileges aside form being a wife, mother, daughter, virgin, etc. Or sometimes the protectoress of her husband's/son's assets: the castle at times of war/siege when the lord is not present; director of his household's activities and servants by being its head overseer of accounts. Therefore, the lord is literally claiming his wife as his effective property through her womb & this is often why when we see women like Daena sleeping with a man not her husband, it is an act of reinforcing her authority or political agency in spite of how she was raised to see her own body.
Think about it: why do we not have a world or society (fictional or not) where even though the wife births a child not her husband's the husband's do not willfully or are "legally" compelled to adopt that child as their own, effectively de-fathering the biological father? Because men want to feel as if they have as close to total ownership over female companionship and labor so they consolidate power to themselves and not to women. Having all these designations of gender and "bastardry" that everyone are compelled to follow makes that easier without expending energy or sharing power. Medieval customs put the social-legal identification of "bastard" from the institution of marriage, its compulsions on women, and their reproductive labor/bodies/uteruses being claimed by the men who are "licensed" to own them. Which is why when we say that neither Cersei's nor Rhaenyra's kids are "bastards" it is true *in the sense that one should not carry the sense of their inferiorty into how we see their innate value as human beings AND none of them have ever been "proven" publicly to be not their putative father's children*, because the purpose of bastardry is to attempt to reclaim the product of reproductive labor and Viserys/Corlys/Laenor/Robert have already done that. To protest about how Robert didn't know about his kids not being his kids is really to protest how he didn't not get the products of Cersei's reproductive labor in the usual male-prioritized business of objectifying female labor that is intrinsic in this feudal society. Whereas Viserys/Laenor/Corlys accepted the products of Rhaenyra's reproductive labor.
All this is also why I really don't care for the impassioned argument of these women were being "unfair" to the system (Rhaenyra) or to their husbands, fathers etc. (Cersei) or them being "liars" or "destructive". Feudalism is itself an objectifying, unfair, unequal system. It is designed to benefit men and mainly men inherently, and directly at the expense of women who risk death itself while a man fathering any sort of kid never risks death. Men lie and destroy the women who birth their children, manage their household, protect their castle, rear their children....and it is all "licensed" and justified under the constructed institutions of marriage, oath-making, knighthood and principles of chastity, virginity, the different sub-meanings of "honor" for men vs women, etc. Men are themselves already objectifying or making an exclusive economic use of their female counterparts as well as going back on their vows (a deal that is still in feudal marriages, even for men) through their socially-allowed extramarital and premarital affairs producing bastards. *Therefore, if a noble woman (or any woman) cheats, it's simply not as amoral as when a man does--it's actually sometimes brave and admirable and a relief to see bc she is taking the risk for the sake of her own autonomy and/or happiness at the expense of a system/man who would exploit or have a consistent upper hand over her, for children he may not even like (Tyrion).*
