It's interesting to me that people read Eloise as being very "im not like other girls" and 'judging' other women, because that's not really what she's doing at all.
From the very beginning she expresses annoyance to Penelope that Lady Whistledown doesn't use her platform to make meaningful change for the situation of the women in her community. She hates the way the women of the Ton are only limited to their looks, and that their accomplishments are only considered in relation to how it may increase their value as wives or mothers. She hates the way she is endlessly compared to her sister, not because she believes anything is wrong with her sister, but because she feels like she is a disappointment just because she isn't the same as Daphne. She loves Daphne, she even supports her and is at times envious of her ease of social grace, but it frustrates her that, because she doesn't have that, she cannot hope to succeed in life in the same way, and it frustrates her that the only value society sees in Daphne was her ability to ensnare the Duke.
No one cares that Eloise is well-read and extremely educated just simply for the sake of her own mind, they care because it means their children won't be stupid. This frustrates Eloise endlessly, and she voices this over and over. She even says to Anthony that she thought the men were meant to be able to hold interesting conversations, and its clear that she's frustrated none of them wish to actually converse with her in any meaningful way. She isn't shaming other women for seeking husbands or positioning themselves on the marriage mart or whatever, she's shaming the system in place, and the men in it, for making it so that the only avenue these women see for their lives is to be wed and bred.
And in truth, Eloise is such a staunch defender of the women around her, always?
When she sees in 201 that Penelope actually enjoys the season and all that comes with it, she doesn't shame her. She smiles, and tells her she no longer has to pretend to hate something just for Eloise's sake. Her very best friend enjoys something Eloise hates, but its not something Eloise would ever shame her for, its just simply something Eloise cannot understand.
When she meets Theo, and he assumes she only wants gossip and information about men, she is horribly offended, but not because he assumes she is 'like other girls', but because he assumes other girls would only be interested in those things, and she tells him as much. She calls him out on assuming so little of women, and shes not shy about it.
When she talks with Kate about being a spinster, she pointedly says that society is failing them by offering no place for unmarried women. She explicitly says that it is the failing of society, rather than the women who decide not to or are unable to marry.
When the man she dances with says that most women he knows aren't intelligent enough for intellectual pursuits, she is furious. When he then makes it clear that he sees her intellect and her scorn of the farce of courtship as nothing more than rebellion, rather than an actual opinion of merit, she just leaves him on the dance floor. His opinion of women as less than, and his view of her belief in women as ornamental rather than substantive, infuriates her and she makes no secret of that.
When the whole Ton is in an uproar over Edwina leaving Anthony at the alter, her criticism is that their whole world is turning upside down because a woman simply changed her mind. She is furious that her family and the Sharma's will face such scorn because a woman decided that a marriage wasn't what was right for her. She is defending Edwina's choices, and in that, Edwina as a person.
Eloise believes that women are brilliant and strong and that they deserve more than what society has offered them. She seeks out intellectual pursuits on women's rights and wishes for women to be allowed an education and hopes to one day see a time when the women around her are not forced to paint themselves up and smile pretty in order to be deemed worthy of society.
And yeah, there are moments where she is clearly exasperated with the young ladies in her social circle. But Eloise never misses an opportunity to defend other women, ever. She wishes the women around her, who she knows are brilliant and accomplished and full of so much more, would just... not be shy about it. She wishes that she could sit with her peers and see that they see themselves as what she knows them to be.
Eloise doesn't hate or scorn other women. She doesn't judge them or mock them for their pursuits. She just wishes they were allowed to be more.