I'm going to try to go into this without getting into the muck of internet culture wars, so that's a plus, but I'm also going to be kinda academic so if that bores you then I guess that's a minus, but I'll try to be brief.
As this thread shows there's two main criticisms, one is of the sexiness itself, and the second is of the reaction by the creator of Quiet to the first criticisms.
The biggest "split" between feminists in the last decades has been the issue of "sex-positivity" (SP) vs. "sex-negativity" (SN). Sex-negatives were the majority of feminists at one time and could still be considered the mainstream of "liberal" feminism. It can be confusing because people look at "feminism" as one thing giving out opposing views when they see something like SlutWalk.
The issue at play is what "objectification" really means and how it applies to society. To put it short, SNs believe that over-sexualization of women by both men and women dehumanizes them, and objectification in the media over the course of years can make many if not most men see women as little more than sex objects to attain for personal fulfillment, rather than people deserving of the same respect and consideration you would give to, say, another man. So it's not Quiet, it's not even every game you've ever played, but rather every game, TV show, movie, magazine, etc. that reinforces that idea, albeit subtly, that a woman's value as a person is decided not just by how "sexy" they are according to society, but also by how willing they are to have sex with men (preferably only one). As a result, girls in bikinis in advertisements, Hooters, strippers, porn stars, the modeling industry, and Quiet along with women like her in games are all inherently bad because they contribute to this culture. To be clear, this is a view that I personally disagree with, but I can give it its due based on its own merits.
SPs, on the other hand, view objectification more fundamentally. It's not the sex or the sexiness that defines objectification, but rather the act of dehumanization itself is a separate issue. There's nothing wrong with Hooters and girls in bikinis or Quiet by themselves, it's only when men and women strip them of all other traits and humanities is when it turns bad. SNs seeing Hooters girls or strippers or porn stars as people just exploiting themselves for personal gain are no better than men who see them as nothing more than sex toys. Women can like sex, they can like showing off their bodies, and them following their own passions and choices in life is what feminism is all about. That being said, men should still treat them with a baseline amount of respect. Just because someone is showing off their breasts doesn't give random men watching ownership over those breasts. Further complicating the issue is that there are many women in the skin trades that really don't enjoy it and may not have much of a choice.
So how does this relate to this one issue of Quiet? The SNs dislike her on principle. SPs have no problem with Quiet, so long as there's an interesting character behind that body, however the justification for Quiet, "she breathes through her skin" was used to silence and "shame" critics (though I can't imagine anyone was shamed), something that was rather shitty of Kojima to do. Had Kojima simply said "I put her in there because she's pretty sexy, but there is a reason," the SNs might have still been mad, but most people who might actually play the game would not have had a problem with it.
