Although I agree that there are several significant changes to Alethi society coming, what with Renarin, Dalinar, and Jasnah defying their societal gender roles, I think that these changes will be slower coming than we expect.
Firstly, the royal family is very detached from the average Alethi at the moment since they are living in Urithiru and, oh yeah, pretty much the entirety of Alethkar is under the control of the singers. Considering that most spanreeds, the main form of disseminating information, are either not available to the general populace or unable to be used due to the influence of the Fused, the culture shift will be less far-reaching, at least for a while. Combine this with fanaticism and how most high-ranking people from all over Roshar generally distrust Dalinar for the rumors of his madness and his former bloodlust and his excommunication, dislike Jasnah because of her atheism and her feminist stances, and are unfamiliar with Renarin (or think he is "weird"), and I don't see this as a large societal change yet unless they can find a way to use the chaos of the Last Desolation to draw attention away from the changes they are making.