It seems like the idea that Anno made Rei as a "screw you" to Otaku is from a creepypasta theory and is not backed up by any actual source. I tried to traced sources for this rumor and it comes up blank. Basically Anno quotes were taken out of context and twisted around into creepypastas. It's about as legit as the Rugrats theory.
And the idea that Anno was shocked that people sexualized Rei. That's directly contradicted by quotes from Anno, and from the fact that Gainax made a trilogy of NGE porn games themselves in the few years after the show aired. The trilogy is called Neon Genesis Evangelion - Eva and Good Friends The Stripping Project! and it's a strip mahjong game (made by Gainax in house). You could also get the stripped girls pics from the game in a series of artbooks (also published directly by Gainax). The only reason I can see for Anno to be dismayed by fan-made Eva-porn is because it cut into the market for official eva porn.
I think it's someone else who disliked otaku who created the theory and dressed it up as "word of god" to give the criticism more teeth.
To paraphrase Anno's only quote on sexualized characters, is that sex sells, anything that gets popular gets porn (he invoked rule 34 basically), and it's been like that since the dawn of time. So Anno's position is that every generation throughout history is sex-obsessed and turns everything into smut. He didn't single out Otakus or modern culture.
The one line where he supposedly blasts otaku culture, if you look at the full quote, he's attacking mainstream Japanese culture, not Otaku. He blasts middle-aged businessmen for reading porn and manga on the train, and says (paraphrasing) "back in the day" i.e. during Imperial Japan, "men were men". He blames Japan's domination by the USA in the post-war period for a general lack of balls and manly men. Again, there's no actual mention of "Otaku culture" being to blame here, and he doesn't even single out otaku at all. He is directly blasting the post-war generation as to blame for Japan's social ills, not the youth culture.
Also if you look into how the character of Rei was designed, you see that Anno didn't really have that much influence. The art designer re-used a girl design from his own previous manga, and he liked a J-rock song called "the girl in white bandages", and that's where the image of Rei with white bandages came from. The hair color was originally brown, but they thought she looked too much like Asuka, and Anno asked for it to be changed. So the artist just inverted Asuka's orange hair which gave blue hair. So Anno had very little input into the overall character design.