
For the people claiming that Emilia's behavior was artificially changed post S1 to make her "more naive".
She lost her insignia while doing street performance in the capital to pay for a kid's meal, and didn't notice until late that Felt had also stolen her wallet.
She also got lost from Ram because she rushed into the downtown of the capital, with Ram being present in the capital when Arc 1 was taking place.
There is another Arc 1 side story called "The Awkward Duo", telling the first loop of the story from Emilia's perspective, talking about how she was socially inexperienced with people of the other sex and didn't know how to talk to Subaru.
In Arc 2, it is revealed to us that due to her lack of sexual knowledge due to both Roswaal and Puck sheltering her, she didn't fully know the meaning of the word pervert.
In Arc 2, there is a side story of her putting a bucket on her head to learn how to sing.
The establishment of her trait of being a dunderhead was always there within the story.
The thing that most people noticed is something that Tappei already answered in a Q&A:
>Q: It’s been a while since I re-read Re: Zero from the beginning but at the start, Emilia lied about her name to Subaru, and you might say her speech was a little more coherent; it seems that she was a bit more mature...
>A: It’s because she was keeping Subaru at a distance, and she was being cautious because she had no one to turn to for help. Once they became familiar, and she learned it was alright to depend on him, she went ‘Hurray!’ and started to turn into a flawed beauty.
it is false that she acts in a "far more mature way" early on that right now: pushing away everyone that she thought could be hurt because of her appearance and upbringing, being insecure about her identity, being less emotionally assertive and letting her emotions control her.
Those are things Emilia no longer does. From Arc 10 of the Web Novel (spoilers):
>>!Ferris: [I d-don’t know… b-but, there’s no other way… I-I, I-I’m u-useless… hk.]!<
>>!Emilia: [That’s not… hk!]!<
>>!…True, is what she had wanted to say aloud. In fact, had this been the Emilia from not too long ago, she certainly would have said so without thinking anything of it.!<
>>!However, she now realized that simply saying that on impulse, without any thought, would not encourage or console Ferris in any true sense.!<
>>!Ferris was amazing. He possessed a truly, immensely special and incredibly kind power.!<
>>!However, Ferris was unable to use this power that Emilia respected from the bottom of her heart for the sake of Crusch, the most important person in the world to him. He was crying and trembling like this, facing such a truly arduous and excruciating reality that he could do nothing about; there was no way she could say that without any thought.!<
>>!Emilia: [It’s okay, it’s okay.]!<
>>!Therefore, Emilia swallowed back down the words she had begun to say, and tenderly embraced Ferris. She continued to embrace him. Continued to embrace him, and continued to hold him close.!<
>>!When Emilia had felt frozen by her own powerlessness, that was what had made her happiest; so, she did the same for him.!<
Showing that she indeed is more emotionally assertive than before.
Another scene from Arc 10, which shows how the present day Emilia is infinitely superior from Old Emilia, who was insecure about her words and whose triumph in the initial speech in Arc 3 was a result of a setup by Puck and Roswaal instead of her own merit, now not doubting her words and not looking at others around in search for validation (spoilers):
>>!"――Emilia?"!<
>>! Suddenly, a dumbfounded voice struck the earlobes of Ram, who had tightly clenched her fists.!<
>! It belonged to Philore, who had her two eyes wide open while keeping the posture of pressing the scripture onto the semicircular table. Blinking her large eyes, she was looking blankly at the center of the room.!<
>! Drawn by that, Ram also looked there, at the witness stand. ――She saw Emilia standing there.!<
>>! She was told things that wouldn't make it strange for her vision to go completely black.!<
>! She was slammed with a despair like having the ground crumble beneath her feet and losing sight of her place.!<
>! Swept away by a storm of unreasonableness and absurdity, it wouldn't have been strange for her to cry and scream.!<
>>! But――,!<
>>!"――My name is Emilia. Just Emilia. The 『Witch of Glaciation』 of the Elior Great Forest."!<
>>! Declaring so, Emilia, still standing at the witness stand, pointed her raised finger toward the heavens and proclaimed.!<
>! It was a pose Ram had also seen many times, the pose an insanely reckless boy struck when he spouted the most foolish thing in the world and started doing it.!<
>>!"This isn't the first time I've been looked at with those eyes of yours. I've been looked at with those eyes so many times before, gotten depressed, and raised my head with a 'heave-ho'."!<
>>!"――――"!<
>>!"So, going back to square one is no big deal. Because I――Because we, will not lose."!<
>>!"Emilia, sama..."!<
>>!"We will not lose. ――Right, Ram!"!<
>>! With her finger still pointing at the heavens, without looking back, Emilia called out to her like that.!<
>! Not looking back to confirm was, frustratingly, nothing but proof of her trust. Emilia completely believed in whatever Ram would say back, and whatever face Ram was making.!<
>! That's why. That's why she didn't look back. Ram had to respond to that trust.!<
>>! She had volunteered herself to accompany Emilia.!<
>! Pushing aside everyone who wanted to respond to Emilia's trust here, Ram, herself.!<
>>!"――Hah! Naturally."!<
She shows more composure when talking to figures of authority, never yields, proudly declares her name even when questioned: the lack of understanding about sex or kisses does not undo any of this very good growth.
It is important to understand Emilia's upbringing: during 6 years of her life, she had no meaningful connection with other human beings aside from a guy selling her wallnuts and people passing out due to her appearance.
She was terribly inexperienced and sheltered. Then Roswaal came and sheltered her even more. Characters need to be internally consistent; all this background cannot be dismissed to turn Emilia into a perfetly completely developed and mature individual, since that would be a plot inconsistency.
Despite all of that setup, she has come a long way so far, and I think it is a disrespect to her character to claim "but she doesn't know sex so she is dumb".