It's quite challenging to genuinely care for 'House of the Dragon' characters, but there is no need to hate them at least.
Both Rhaenyra Targaryen and Alicent Hightower are pretty complicated personalities, to say the least. The first one has been proclaimed a king's heir, even though the king, like the rest of his court, is pretty skeptical about a female heir. The second one has been coerced into an unwanted marriage with the said king, and even the status of the Queen does not seem to make things more enjoyable.
The two young women are definitely far from nice girls, but both of them fall in line with the show's general love for morally grey characters. Rhaenyra and Alicent both do questionable things sometimes, but hating on them is not exactly a good idea – not least due to their ultimately suppressed position.
According to fans, Rhaenyra and Alicent are essentially victims of how things are done in Westeros.
"Listen… both Rhaenyra and Alicent are victim of the patriarchy there portrayed. They aren't wrong, they just don't have the power TO CHOOSE. And that sucks. And that's why I'll always be loyal to them, it doesn't matter what happens. They deserve so much better." – @rhaenicents
Naturally, not everyone is ready to agree with that. When it comes to Rhaenyra, some people think she just fails as the king's heir.
"After 4 episodes of House Of The Dragon it's safe to say that they only were able to make it this way because Rhaenyra looks like she's being held down by the patriarchy but actually she's a worthless heir who feels she should be handed the throne because she deserves it." – @upstatefederlst
Still, many people agree that the pressure of patriarchy in Westeros is felt when it comes to both characters. Even when they appear to win because of it, it seems that their victories are nowhere near being actually enjoyable.
"Alicent was complicit and did benefit, but it's not like she had the power to refuse her father or the king so I still feel for her and think her a victim of patriarchy. Otto was also obviously sexist towards Rhaenyra and Alicent, and women in general." – @jennyfromretail
However, even those who agree with that argue that different female characters have various ways to react to the Westerosi way of living, by either being complacent or standing up against it.
"There's also a choice in standing with other women against the patriarchy or enabling it & punishing other women. The likes of Cersei and Alicent do the latter and tho they have reason in that world there's no point in excusing their behavior as anything but." – @duskglo
The showrunners, in turn, have touted 'House of the Dragon' as a show that highlights and takes a dig at patriarchy, with the creative team pledging to explore misogyny and sexism in the series. This has caused various reactions – from rounds of applause by progressive viewers who crave more women empowerment in such series, to accusations of bowing down to "woke" tendencies from more conservative viewers.
'House of the Dragon' is currently streaming on HBO Max, with new episodes arriving every Friday.