I ask that you please read through all the evidence before anything else.
ANIME
The Episode 24 Filmbook clears up a lot of issues with the English translation of Shinji and Kaworu's talk that create ambiguity. Most notably because in Japanese Kaworu uses explicitly romantic language ("I was born to meet [逢 for "meet" has romantic connotation] you") towards him. Anno was not trying to go for platonic friendship. In this way their relationship is blatantly portrayed as romantic.
庵野秀明 パラノ・エヴァンゲリオン (Evangelion : Hideaki Anno : Parano) is an official anthology containing interviews and background info from Anno with a big focus on Evangelion. Here is a page from the book
Translation:
Nagisa Kaworu The fifth Eva pilot whom Seele sent in. To Shinji, he was both the very first friend he could confide in as well as a same-sex romantic interest. On the account of his true nature as an “Angel”, he attempts to merge with the First Angel, Adam, ensconced in Nerv’s underground, to trigger Third Impact. Driven at the far end of his anguish, Shinji kills that beloved friend of his with Eva Unit-01.
The JUNE magazine Anno interview released after had these excerpts:
Interviewer: Did you stop Satsukawa-san when it looked like he was going to go berserk, Director Anno?
Anno: No, nothing like that. Satsukawa-san’s atmosphere remains in the script. (the Episode 24 drafts) Satsukawa-san’s original script had more of that sort of meaning and was JUNE-like.
Interviewer: For example?
Anno: I’m the one who went and set it in the bath, though. In the original script, the two of them were swimming naked in a river.
Interviewer: In broad daylight?
Anno: I don’t know; it might’ve been at night.
Interviewer: At night, while showering in the moonlight?
Anno: I don’t know. There was a beautiful picture of the two of them swimming in the river. As might be expected, this was what you’d call above my tolerance level.
Interviewer: The version of the ending, “FLY ME TO THE MOON”, with two boys.
Anno: The producer also rejected it, unfortunately: “As might be expected, I just can’t do this.”
Interviewer: Were there other scenes like that?
Sato: Hmm, he had a cello, right? Together… “I’ll play the piano, so you play the cello!” he said. At night, in a classroom, Kaworu went first, and he was playing; when Shinji softly peeked in on him, “Can you do something, too?” “Next time, let’s do it together.” It had that sort of feeling.
--
Anno: [Kaworu's] image is a little different. Well, as a character, Ishida-kun’s voice was incredibly good, so I wondered whether the stuff that I’d simply thought up on my own wasn’t a little insufficient. I wanted to make him someone that could be loved by anyone, an incredibly good person. By the time Shinji saw him, there was nothing he could do but get a complex.
In 1997, KAWORU NAGISA was lost beforehand in End of Evangelion is another official anthology. Transcript from one of the pages
The moment Human Instrumentality Project began, Kaworu’s form appeared in front of him again.
But, is this still the same “him”——
"You have been there all along?"
The question melted in the air. He whispers to Kaworu, facing the lover that he is about to lose.
Another transcript
“I was attracted to him.
Deep in my heart.
I don’t know when it began.
I really don’t want to fall in love with a boy like that.
I really don’t want to have friends anymore.
Even so……
Why humans have to be attracted to other people so hopelessly?”
So let’s make a wish.
“Please let me redo again.”
No matter how many times
“Thank you” and “Goodbye”
Wishing for reunion and leaving.
Now here I want to clear up a common misconception with previous claims that Shinji was desiring Asuka's tits. I won't argue that Shinji is only attracted to boys in the anime, but this evidence is wrong because those were Misato's because he conflates her with Yui/the mother figure (such as when he sees Yui with long hair) and so he was desiring the breast of his/the mother - a major theme in Eva we see especially with Shinji by various imagery/specific shots throughout the series and EoE. He wanted to "return to the womb", a safe place he can't get hurt. That scene had everything to do with his mother issues. Even more obvious when the following sandbox scene has Misato watching as the mom.
Also, this happens right at the same time Kaworu jams the Lance into Shinji-01's core and Shinji sees himself as female. Here is a more clear undisputed visual
Folds of flesh surrounding Unit 01’s Core. Notice the flesh looks just like a vulva.
And this [the core] is of course the metaophorical vagina.
Penetration...
Orgasmic bliss. The drafts make the core-vaginal symbolism very clear:
REBUILD
Now in Rebuild I argue that Anno purposefully took out scenes where Shinji is attracted to girls to show that Kaworu has really become is only love interest. It's very clear looking at the Studio Khara Calender 2014:
This is Diptych of the Duchess and Duke of Urbino by Piero della Francesca. Below are the paintings on the back of each portrait, Allegorical Triumph of Federico da Montefeltro and Allegorical Triumph of Battista Sforza by Piero della Francesca. Accompanied by Angels and the Cardinal virtues, the husband and wife return to the palace of Urbino. Fedrico’s cart is pulled by white horses, Triumph of Love, while Battista’s by unicorns, Triumph of Chastity.
Federico da Montefeltro, nicknamed “the Light of Italy”, is a landmark figure in the history of the Italian Renaissance. He often strolled the streets of Urbino unarmed and unattended, inquiring in shops and businesses as to the well-being of the citizens. His academic interests were the classics.
Battista Sforza received a humanist education and was fluent in Greek and Latin, giving her first Latin public speech at the age of four. The poet Giovanni Santi described Battista as “a maiden with every grace and virtue rare endowed”.
Her uncle Francesco Sforza arranged for her marriage to Federico da Montefeltro, who was much older than her. The wedding took place on 8 February 1460, when Battista was thirteen years old, and she acted as regent during her husband’s absences from Urbino.
Their marriage was a happy one. They were described by a contemporary, Baldi, as “two souls in one body”.
Battista fell ill three months after their seventh child, and died in July 1472. After the death of Battista, Federico spent much of his time in the magnificent palace in Urbino.
Maeda he tried to imitate Francesca’s style by giving Shinji and Kaworu squashed profiles. Look at the jawlines, he drew them exactly like Battista and Federico. Notice Shinji's strong outline.
The landscape background and profile portraits are all classic Pre Renaissance conventions. Best of all, anyone back then would’ve known that these two people were married because they’re facing each other. Sadamoto and Anno use Tanabata references that are easily recognizable to any Japanese person. And then you get Maeda who likes to use historical imagery to symbolize they’re soul mates.
Anno said the posters were fundamental to the movies. The 3.0 poster features Tanabata, "the meeting of the deities Orihime and Hikoboshi, represented by the stars Vega and Altair… Star-crossed lovers separated by the Milky Way.":
Orihime and Hikoboshi loved each other intensely, but were only allowed to be together once a year. Not only that, but Shinji's and Misato's VAs confirmed in a 1997 interview that Kaworu was Shinji's Hikoboshi.
Notice also the color of Shinji's earbuds. They’ve always been black throughout the franchise but for this poster only, they’re red at the end and extend to Kaworu. {The red string of fate}. The act of sharing earbuds alone is something that couples do in Japan. So even people that are unfamiliar with the series think that they’re together because they’re sharing the same set.
One of the earliest teasers had the husband and wife tree actually shaped like a heart.
Well that's the major points. There are many other evidences I could add here, but I wanted to start with these.[/i]