So, I have wondered why so much in Eva seems to work by pure accident and chance, while other things seem to be completely deterministic (most blatant example: Asuka's fight against the MP-Evas. No matter what she (or anybody else except the Trinity) does, she is always going to die, one way or another, at the latest point when Instrumentality is started). I also wondered why Gendo seems to not care about anything, and doesn't act as efficiently as one would expect from a master schemer. He instead seems to be a fanatic believer in his eventual victory. I truly do NOT want to start a Nazi discussion or draw any other parallels, but he reminds me of Hitler in his bunker. Right up until the end, no matter what happened, the Endsieg was going to happen. It's even a meme: With the attack of Steiner, everything will work out. That's why it doesn't matter how much Gendo neglects and traumatizes his son, or that he lets him go - twice. He just has to believe strong enough in his Endsieg, and that will make it true. Asuka losing her ability to pilot? No matter, something else will swoop in and fulfill his destiny. I also wondered why SEELE seems to work the same way: Sending Kaworu, for whatever reason, is such a huge risk that only religious fanatics would even consider it. I put that down to the fact that they actually believe in the absolute accuracy of the Dead See Scrolls. Not telling the MP-Evas to kill Asuka outright? Doesn't matter, the outcome has been foretold, they think.
And in the end, everything works out for both of them, by pure accident (SEELE gets their Instrumentality, Gendo gets reunited with Yui) - except it isn't an accident at all, and neither is it some cosmic fate in the traditional sense. Many things in Eva don't make sense on the surface. For example, why don't the angels attack Germany, where Adam is held? Why doesn't Sahaquiel just nuke NERV from orbit? How come Unit 01 manages to kill Leliel two seconds before the UN drops 998 nukes into it? How come Shinjis says "Everybody can just die", yet nobody dies when his wish is "granted"? How come Second Impact didn't make the earth uninhabitable? This all makes sense with a shift of perspective, where we are not seeing the epic battle between the angels and humanity, SEELE and Gendo, or the internal conflict of the characters affecting the whole world, but a mere stage play put on by the Trinity.
I hate the idea that Rei (and Adam as well, since he is a SEED just like her, and possibly the angels) can travel through time, but I can't ignore the tells that she actually is capable of that, so I have to conclude that she can. The implications are far reaching. First of all, it throws causality right out of the window, as there is no "before", "after" or "at the same time" anymore. It also means that there are infinite, parallel realities, since every possibility must play out if you are able to change the past. Flip one single quantum to another state, and you have a new reality, which spawns infinitely many of its own (unless the universe is completely deterministic or Roger Penrose's idea of re-merging realities is true, but that is a little too large in scope to discuss here, and I am not even qualified to do so

).
Since time also ceases to be a limited quantity with time travel, even in the theoretical sense, every possibility, no matter how unlikely, WILL happen. And has already happened, since "before and after" cease to have any meaning. When Yui merges with Unit 01, she suddenly becomes aware of all that. Or rather, she never was unaware of it. It gets complicated. From the Trinity's perspective, everything makes sense now. Everything already has happened (or is happening in this moment, or will happen).
That means that their perspective is just unfathomable to us. Basically all human concepts revolve around causality and time, but none of that matters to them. Cruelty or kindness only matter if they change your future, but if you have infinite futures and infinite time to contemplate, you are already over it before it happens. Death means nothing, as it isn't an event in your future, it has already happened to you. Or rather, you are always alive and always dead. The Trinity can not grasp the human experience of causality and time as a one way street any more than I can grasp being a horse or a dog. I can imagine being one, but I can never experience it. I can not even experience being another human. I can just, as a philosophical exercise, play make believe.
Which is exactly what the Trinity does: They want to get the angels to another planet, so that humanity can have the earth for themselves. (Well, that's in itself loaded language: They don't "want", they already "have". They need no "Why", because there is no way it won't happen. They just amuse themselves by pretending otherwise.) It seems like a coincedence that Sachiel attacks at the same time that Shinji comes to Tokyo 3, but it isnt. It is part of their play. That's why he casually strolls towards the gunfire, without any haste. Since "good" and "bad" are linked to causality, there is no distinction between them anymore. There is just experience and non-experience, with the first being preferable. The Trinity wants Shinji to experience something, so he is welcomed by an angel on arrival. They never wanted to kill him, they wanted to play with him: When he doesn't, Yui finishes the fight. Sachiel embraces her and self-destructs, as that was his goal all along: Free his immortal soul by shedding his body for a little fun and do something good for Shinji: Give him an experience.
This continues with the other angels: Ghagiel swallows the battleships, because why not? Seems fun. Yui bursts out of Leliel to offer a little surprise; she would have survived anyway, along with Shinji, as that was the plan, and she can freely choose a timeline where she does. Maybe she just likes the aesthetics? Sahaquiel wants the trio to feel like they achieved something, that's why he lowers himself to be killed. I can totally see him singing "Why did this happen to meeeee?", feigning surprise while he explodes.
But what does this look like to Gendo and SEELE? It looks like, no matter what, their plans work out, as if some divine intervention makes their hopes come true. Except that their plans don't matter at all, and neither do their actions. When Gendo sends Shinji away before Zeruel attacks, it seems totally counterproductive and dangerous. But there was no danger at all. He possibly just believes that Yui will save him, like she did many times before when she took over, to protect Shinji or whatever plans she has. Except that she doesn't even need to, as the Trinity already decided what will happen in this little pet reality of theirs.
It seems strange that Yui only reacts after Asuka dies - why would she put Shinji through the extra pain? So that he triggers Instrumentality? Well, no. She knows the eventual outcome. She's just offering him a new experience. This isn't cruel in her eyes, since in the end, he will wake up with Asuka on the beach, and thanks to her perspective, he already IS on the beach while Asuka gets skewered. She also sees him living infinitely many lives, so it really doesn't matter if she screws up one of those, as there is also one where Asuka confesses her love for him directly after Kimochi Warui and he is happy ever after as everything is sunshine and roses. Rei doesn't grant Shinji's wish to let everyone die because, in his future and her now, that specific Shinji regrets it. In essence, his wish doesn't even matter: Instrumentality was happening either way, since it wasn't his decision at all, but the Trinity's. When Yui asks Shinji if he will be alright, she is not asking out of concern: She is curious how that specific Shinji in this specific timeline sees things, since she forgot how to have a limited perspective. He has no choice anyways. In his future and her now, she already is on another planet playing angel-kindergarten while her son is rotting away on that beach (but he is also fine).
Ah, I mentioned the shifting of earths axis. There are infinitely many pasts that lead to Second Impact, and infinitely many futures that spawn from it, but humans can only experience one timeline. When Second Impact occurs, the Trinity shifts earth to a new timeline where the earth always was aligned the way it is in NGE. The south pole still melts and sea levels rise, but the causal chain leading to that happening has nothing to do with the timeline humans remember. There just happens to be one timeline out of infinitely many where everything stays the same (people, history) except for the alignment of the earth, giving the impression of continuity of some form, even though that continuity violates physical law and causality. The obvious objection is that humans would then remember that timeline, not their original one. But if you have infinite realities, there is also one where humans remember a timeline different from the one which is actually their past. Well, ALL of them are their past anyways ...
Same goes for Third Impact: As Mr. Tines likes to point out, there is no way that the earth is inhabitable after that, for many reasons, from Rei impacting the earth, to even microbes being tanged and the implications of that. But thankfully, there is one reality where only humans get tanged, where Rei impacts the earth but nothing too serious happens, yet everything still looks like that's what should have happened. If you can navigate infinity, that means that "likelyhood" or "chance" become meaningless. And we, as the audience, get a glimpse of the perspective of the Trinity, which watches and plays with that specific timeline, as there is stuff happening there, and experience is better than non-experience. If something doesn't work out like they want, they can just go back and change it - or rather, they already did, infinitely many times, and we get to see one end result.
It also explains why Rei self destructs: She is replaceable, in more than one sense. There always is a Rei, in the past or in the future, which is the same as "now" for her. It seems like a big choice for her, but it isn't: She is acting. Even if she isn't, and that specific Rei is unaware or her nature, there are infinitely many other Rei's in infinitely many realities influencing infinitely many parameters infinitely many times so that Rei II self destructs in that specific timeline - because why not?