In my humble opinion....
(I swear its objectively written as a reader)
I'm guessing its because this is Lydia's true nature due to her upbringings and cruel environment. She is of her own control, not inside a story or manipulated by some magic. And she in the past never gives her daughter anything apart from taking Lyrica with her, but eventually she marries her off to old noble. She as an adult, lives as a drunkard, made lyrica work for her and took her money, didnt feed her, hits her, and made lyrica sacrifice herself for her in the end, it was only then that he realized Lyrica's love for her. In this timeline, she "redeemed" herself though.
Meanwhile Claude in truth, grow up as a quite decent king despite the harsh past he has. Then he lost his memories and was manipulated by a curse magic. Then again, the claude that killed her daughter was part of a "story".
And you cant compare lydia in current timeline vs clause in the current timeline.
Lydia remembered everything that's why she can redeem herself, while claude don't. Its still the same him, but different circumstances and situations because athy took actions.
In the current timeline where he didn't know anything, and didn't have any memories, he was never cruel to her and even loved her, apart from when he was manipulated by the curse and with no memories when athy is teen. He did ignored athy for 3 or 4 years, but athy was still a princess with a loyal servant next to her. She was still given place to live comfortably. Athy never starved, and was never hit. But even when they met and interact, he was unexpectedly gentle and kind. That's how athy and the reader grow attached to him as well.
That's the difference, that's why people have some spot for claude, but find it hard to forgive Lydia. Claude was the "victim" but Lydia was one of the "perpetrators".
For the note, I don't hate Lydia, and its not like im a hardcore fans of claude either. Its just from my objective point of view, it was very understandable why people forgives claude and hard to Lydia. Its not because he was a men of any double standard. Its just how lydia and claude was written.
Had claude ever done the exact same thing as Lydia in the past, he will be even more hated than Lydia ever does. The difference is, Claude never hit, starve, or make her daughter works to the bone.
claude wasn’t present in the beginning but he never hit his daughter, starved her, worked her and stole from her, sold her off to an old man to get graped. lydia did ALL this for power. when claude DID hurt her when her daughter was a teen, it was because he was being manipulated by magic while lydia did all that with her free will. thats the reason why lydia gets so much hate. not because of misogyny lmao
Seeing how she is, I’m comparing her with how people treat her compared to Claude from Who Made Me A Princess, which is similar to how Lydia’s story is as well. The double standards is insane, cause most people are willing to forgive and praise Claude’s redemption just cause he’s a man.