I'd like to counter this by saying that Gender Stereotypes != Sexism. I think all of us are aware that games like Zelda have gender stereotypes at play. Sexism is a much stronger claim than "reinforcing gender stereotypes".
Uh, by definition, It kinda is. Sexism: prejudice, stereotyping, or discrimination, on the basis of sex.
What we can argue is that there's degrees of sexism -- that a gender-stereotyped trope isn't the same as a professional prejudice or an outright slur; that sexism in the cliches of a story is way less harmful than direct sexism against an specific individual... but that's way off topic.
If someone says they're going looking for sexism, and there aren't many big major things for them to find, then they're going to deal with these "minor" cases...
It's much like the violent video game controversy of the past (and still somewhat today, unfortunately). No, violently murdering people left and right and getting cool brutal finishing moves done does not make me a violent psychopath, or even condition me to be more as such. Likewise, playing games where men are in positions of power over women does not lead me to believe it should be the case.
Who's suggesting that sexist games make people sexist?
The examples that people usually give about why these stereotypes are harmful are quite different -- not that boys playing Mario will be so affected by them, but that people tend to identify with role models of their own gender, which means that girls playing Mario will only have the useless damsel as the present role model. These critics are just pointing out that it would be nice for Princess Peach to take an active role in more of the Mario games (like in Mario Kart).
These stereotypes are like McDonals - it's ok if you have a balanced diet, but if you entire diet is this junk, you're not going to be healthy.
Having princesses being rescued by white knights is fine... but if every childhood story is based around the same stereotypes, then they're going to sink in and not help to produce a well rounded person. You need a balanced diet of media consumption.
McDonalds themselves tell you not to live on their food - that you should mostly eat good stuff and occasionally eat their products... but it's still ok to criticize McDonalds food for being full of preservatives or cheap/reclaimed meat or whatever.
Such criticism against McDonalds isn't a demand for them to desist or change, but a checklist of improvements that you would make (unless of course, if you accompany your criticism with a protest movement...).
Likewise, when someone specifically goes hunting for subtle sexism and writes a critique based on it, it should be taken as a checklist of improvements that they would make, or that you can pay attention to if you want to address subtle sexism in your work.
That kind of critique is not something that we need a "movement" or "consumer backlash" or outright hate campaign to protect us poor developers/gamers from. If someone makes a checklist that you don't need, you simply ignore it, not grab your pitchfork and join a lynch mob...
Ironically, we're seeing a protest movement that seems to be aimed at crushing critique and discussion, while claiming to be about exposing bias... :(