As far as I can tell, the Rei theory stems from a sensationalist
Atlantic article talking about Japanese mass suicides, and trying to link that to Evangelion's Rei being a depressed character. It contains some of the article author's assertions, mixed with quotes from an Anno interview. The author makes some factual errors about anime in the article, and it was the author who made the Otaku = Pervert connection. Anno doesn't even mention the word "Otaku" anywhere in the interview. So, rather than being a case of Anno criticizing Otaku for sexualizing things, the real culprit is the writer from The Atlantic trying to "sex up" the story about Japanese suicides.
Yeah, Anno does slam Japanese people in the interview. But his target of choice is
salarymen who read porn and manga on the train, i.e. he clearly slams mainstream Japanese culture, not otaku. As for the sexualization of characters, there's another Anno interview somewhere. What he basically says is that "anything that gets popular gets sexualized. It's been like that since the dawn of time". Yeah, so he's saying that it's human nature to sexualize things. Nothing specific about Otaku.
What the interviewer seems to have actually asked Anno is "why do you think a character like Rei resonates so well with the Japanese people", to which he answered by talking about how Rei is a profoundly sad / damaged character who feels powerless over her own fate, and that the Japanese national psyche was damaged by the aftermath of WWII, when they became dominated by the USA, thus did not control their own fate. So in other words, he actually said that Rei
appeals to the Japanese because they see themselves reflected in her. If you read the parts Anno actually wrote, that's the only context that makes sense.
The version of this that turned into "Anno thinks otaku are big manbabies who only like Rei because they are scared of real women" is complete bullshit in other words.