Penelope is not a feminist. Penelope is a capitalist. She's a businesswoman. She can be a feminist character, as in, a character who is a well rounded woman with agency and power and flaws that we can uphold as good representation of a full woman, without being a feminist herself. When people claim Penelope is a feminist, they do so partly because of her intersection with Eloise, and partly because she makes her own money. But I think the truth is that Penelope really isn't interested in pursuing or fighting for the rights of women. Which is why her speech to Colin in their wedding fight felt so jarring. Penelope never used Whistledown to uplift women or give them more power. She was never a scholar of feminist study.
She felt how their society stifled her, but she didn't have feminist criticisms of that society. In many ways, she escaped from beneath the thumb: she makes her own funds, has her own pursuits, and saw getting a husband in S3 as a way of securing her freedom. But even that felt strange and forced, because Penelope was ALWAYS interested in marrying for love. She loves dances and society and the pomp of it all. She's a romantic. She was never in full agreement with Eloise in fighting for women in general to have opportunities outside of marriage, because for Penelope, she's fine with marriage being the expectation. S3 just shoehorned in that she wanted a husband for the sake of freedom from her mother as a plot device to push her and Colin together faster.
In the same way that Penelope had a friendship with Gen, who is a working woman, without being part of the working class herself, Penelope has a friendship with Eloise, who is a feminist, without being part of the feminist movement or ideology. Penelope didn't use Whistledown for feminist purposes, she used it for personal and capitalistic purposes. Whistledown was her voice and her means of making money, it was her craft and her hobby. She didn't care to use it as a way to give voice to the voiceless or disseminate feminist ideology. Whilst gossip CAN be used to provide information to women so they could navigate the world more safely and with knowledge, that wasn't her pursuit, either.
That's also why Eloise's opinion on Whistledown changes in S2. In S1, she's enamored by the idea of Whistledown: it is proof that a woman can find power in society without having to marry, hope for Eloise that she could escape patriarchy's clutches. But by S2, she's displeased because she starts asking herself 'and what is she doing with it?'. Eloise sees that Lady Whistledown, though she achieves freedom that other women in their world don't have, falls in step with patriarchy in the same way that their society does. It's not a feminist publication. That's why Eloise starts pursuing other avenues to explore her feminism, and is so eager to find herself in feminist discussions with working class people. It's the first time she has an audience and connection with people who are also interested in women's rights. She didn't find that with Penelope because Penelope isn't interested in women's rights as a collective.
And I do kind of wish that the show acknowledged that instead of trying to retcon it. The feminist speeches from and to Penelope in S3 didn't land right because they had no real foundation. Portia's whole 'women don't have dreams, they have husbands' thing was used to make the audience sympathize with Penelope to keep LW and frame it as a feminist pursuit. And in many ways, it is! Women making their own money IS feminist. Just like divorce and abortion! But Penelope herself is not a feminist, so her qualms with it are not that ALL women should be able to make a living, but that SHE has made a living, and she did it through Whistledown. That's also why her fight with Colin after the wedding breakfast feels so hollow. She falls back on 'you wouldn't understand because you aren't a woman', when she never felt much kinship with women as a whole, regardless.
I think it all kind of got framed weirdly and got very murky. Colin wasn't asking Penelope to give up LW because he's her husband and wants to lord his opinion and will over her because she's his wife and thus his property. None of his concerns were because she was making her own funds or was an independent woman (sure, he was insecure about what he could provide for her if she didn't need him, but that's not why he was against LW continuing). They had just been threatened by the Queen of England at their wedding reception because she was pissed at LW and on the pursuit. Penelope framing it as a feminist issue felt tone deaf. The writers turned it into a feminist concern when it wasn't. The overarching narrative, women should get to have careers and money of their own, IS feminist, but Penelope getting pushback about Lady Whistledown specifically and wanting to hold onto it is NOT feminist. Does that makes sense? Even if she is a woman and LW is her career, it's not BECAUSE she's a woman with a career that Colin had concerns.
I know that's a bit of a quibble and getting into the weeds of things, but people attributing Penelope as being a feminist with feminist pursuits, as I see them do sometimes, just doesn't hold water. Penelope is a woman who's narrative can be interpreted as feminist, but she herself is not a feminist. Eloise is a feminist. Arguably, she's the only feminist main character we have. Eloise fights for the rights of women. Imperfectly, but still. Penelope fights for the rights of womAn, singular. Namely, herself. And that's okay. This isn't a criticism of Penelope.
Not every female character should be or is a feminist. But feminism is a specific political ideology, and Penelope just doesn't subscribe to it.