Modern criticisms of female characters seem to fall into one of two broad categories:
(be patient with me as I attempt to translate a vast grey area into something binary)
1) Feminist Media Revolution
I name this perspective from a place of appreciation. Neither "feminist" nor "revolution" should be considered dirty words when it comes to discussing media culture-- media is, after all, defined by its consumers. This camp is composed of arguments across a range of extremity levels; however, they all aim to expose how female representation in the media is unsuccessful.
The Feminist Media Revolutionaries are invested in drawing attention to aspects of media the common consumer may not notice.
Extreme ends of this spectrum, as with any range of opinion, rarely come across as productive. This is often where the "man-hating" assumption of feminist critics comes from.
2) Leave Well Enough Alone
I had a hard time finding good sources to discuss for this group of opinion that weren't political. But I've certainly had a good number of these conversations in person, and I'm willing to bet you have too!
The Leave Well Enough Alone crowd are certainly happier than the Revolutionaries. This group appreciates media without thinking too hard about it. It is "entertainment" after all!
In my personal experience, most people who say the media portrayal of women doesn't need to improve are either (1) men, or (2) women who identify with the sort of female characters we commonly see.
There's an extreme end of this spectrum for sure, who prefer traditional gender roles in media, but they're rare. Just as rare as the other extreme. Most Leave Aloners are just content and that is a perfectly valid way to feel!
I present both of these ends of the critical spectrum to you in order to illustrate the importance of a happy medium.
The Feminist Media perspective can be essential to understand subtle ways the media is unequal in it's treatment of women. Take for example, Rowan Ellis' argument on the use of viewpoint in cinema.
Ellis points out how the cinematic device of "gaze" in order to bring attention to subtleties in film making. These devices, she says, are, "what we take for granted as 'just how cinema is made.'" Her article discusses how all parties are disadvantaged by this, regardless of gender or sexuality.
On the other hand, the Leave Well Enough Alone crowd reminds us to question how much children internalize media messages, and how much they're just learning from their parents. This group can highlight the importance of real life interaction and how media either reinforces or defies this, rather than shaping it.
Simple Google searches articulate this variety in opinion. Disney princesses are, "good role models," or "bad." Female characters in general are either "hated," or "sexualized."
There is an obvious discrepancy, and for this reason I believe reading Feminist criticisms is important. However, the Leave Well Enough Alone crowd gives us the optimism we need to appreciate how far female representation has come in media.
We control how we respond to the media, it does not control us. But it is made for the public to consume and should cater to the demographics of its audience.
So if, for example, you want [better nerdy female characters] you have every right to ask for it.