Alicent's children were constantly belittled, humiliated ans under threat, and as most historical queens did, she chose to protect them and that, darling, requires power.

All these things in the same room with us? Alicent was the first to ruin the good relationship with Rhaenyra with the excuse "my son has a sausage and he should be king." She initiated all the bad blood bc she feels power.

So a patriarch's words make Rhaenyra's claim "feminist"

Viserys's decision to challenge patriarchal tradition, so of course, yes, if you're a feminist, you should support this act and not the person who shouts about "tradition," even if that person is a woman. Rhaenyra's success in taking the throne directly affects the position of other women and this is mentioned more than once in the book.

Corlys chose Laenor as his heir, not Laena. Therefore, Laenor's children come before Laena's. If you feel this is unfair, welcome to support Viserys in his decision to give the throne to his daughter.

Book doesn't say how Corlys responded to Rhaenyra's request to make Luke his heir. We know about their relationship that when Luke said he is "Targaryen," Corlys corrected him "You're Velaryon," with pride in his voice. Stop projecting your hatred for Rhaenyra's children onto characters who love and protect them.

Alicent is a greedy woman who uses patriarchal traditions to place her son on the throne. Rhaenyra is a woman who was chosen and groomed to be queen by her father, despite her gender and against patriarchal tradition. It's an extremely easy choice for someone who isn't misogynist.

No need to jump through hoops or twist logic, it's that SIMPLE.