I always thought that Shinji, especial from the rest of the characters, was a representation of what Anno hated about himself in his bouts of depression when he was younger, and possibly even now. A life lived fluctuating between elation and nearly endless depression. I mean, Evangelion has always seemed like a deeply personal deconstruction of Anno, otherwise it wouldn't be as great as it is, at least to people who can empathize with the ideas.
Does he hate otakus? I don't think so. It's clear to me that he wouldn't have created Evangelion if it wasn't important to him and as a message to otakus (he being one), to realize that the world can be more interesting and worthwhile to experience than jerking off to cartoons. The two endings of the original series seem to represent that, ie., Shinji decided to live in a world of both elation and suffering (truth) rather than in a state of "artificial" bliss where nothing bad ever happens.
Anno didn't have to make Evangelion. He doesn't have to do anything at all, but he "chooses" to. Why would he do anything? Because he still cares. It aligns with an idea that's prevalent in both series where Shinji accepts any form of communication from others as being worthwhile. When he doesn't get what he wants, he reacts violently like a child (ie. a younger child, only being able to express themselves in extremes) instead of learning from the experience and continuing to "do better things".
With the Rebuild, I do get the feeling he's 'softened' or "calmed down" over the years, as is often an observable case with anyone that more fully understands how the world works and their own behaviour. In the act of aging, there are many things you have no control over. A pain in your lower back that keeps resurfacing that you never had as a teenager. Balding or gaining excessive weight after bearing children. Gradually losing one's sexual drive to be temporarily replaced with mid-life crisis devices. Wanting to be a child again because of one's self-defined excessive awareness to one's own suffering. As such, people tend to become more gentle both physically and mentally. So, he creates Rebuild which often seems like it deals less with existential quandaries and mental exercises (mind-fuckery), and devolves more into 3D bombastic battles with Shinji being a listless or confused dickhead, but still a sympathetic character, at least to a point before one can get 'annoyed' by the real net-negative human attributes he's representing sometimes.
Secondarily, Anno wants to make money and he knows he has an audience for his work who are willing to pay for it. They pay for it because they care. They pay a lot of money because his material connects with them (I only own the DVDs and not extraneous merchanidise). And many consume the Evangelion machine because it all says something with worthwhile utility.
No. He can't possibly hate otakus. If he did, he wouldn't have done what he's done and will seemingly continue to do. Hating something that doesn't necessarily have to affect you is, again, something a juvenile would do. Do people honestly think Anno is that juvenile? Yes, because people are naturally inclined to efficiently and irrationally reject things that don't align with their perspectives or that which entertains them ("It's not fun, Mommy"), so it's no surprise that a subset of anime fans would cowardly attack his fiction. Are they right? Maybe some of the time, but everyone can be right even when they're mostly wrong.
At some point, labels are over-simplifications of what people are, but then people are not as complex as they think they are. Often, most will wish to appear strong, intelligent, or worthwhile, when that's never been the case for anyone at all. We're fickle creatures.
I would urge not using the word "hate" when you're not implying what would be the result of hate: A complete indifference of suffering or active destruction of things they hate. People who "hate" are often fulfilling a definition of themselves that they never had a choice about, which is often ironically hypocritical (at least to an audience that is aware of it). Words have meaning and should be used with more care, despite what the echo-chamber of bad ideas that the internet can be, where having and expressing an opinion is more important than being right. Intentions are a significant part of the puzzle that are often ignored to satisfy a sense of righteousness, when there is none to be found.
Just ask, what are Anno's intentions? It seems it's mostly good will. If people can't see that, well, bad for them, for them, for them, for them.