IMO the only inevitable "redemption" needed is Yukio changes his recent opinion about Shiro (probably also the Order), and fight for human again.
I made this experiment: I took the whole BTS arc (and aren't we gonna mention we're STILL in it? (chapter 97: beyond the snow part 6 (crap, this thing's getting really long))) and read it all at once.
Okay. Premise: let's say the "Yukio before trying to shoot himself in chapter 93" and the "Yukio after that" could kinda be considered 2 different "persons" since right after that attempt Yukio decides he's -definitely- done with his fake act for good and starts to literally do/say what the heck he feels like without giving a shet anymore. But, I think it's kinda safe to state Yukio was kinda starting to give signs something was already in the air before the BTS arc began. Like, through laughing in the face of people, pointing guns, making scary/evil glares and such. So, what I want to say is, Yukio was already "in the process" of a (dark) "change" before this arc.
But, in chapter 93 he opens the usb contents and... um, dunno how to put it. I never stop to consider it, but it feels somehow "incredible" (imo) how emotional he suddenly turns after finding out about S13. Like he's briefly out of his "cold and numb" state and he can feel emotions again. It's like those big revelations caused him to abruptly snap out of his "insane" state (temporarily). Maybe it's not something THAT biggie. But after chapter 90 and before chapter 93 I doubted Yukio could still be able to get emotional.
Now, yeah, as I said, the Yukio after chapter 93 and the Yukio before chapter 93 are on two different levels. But my point is: the "slightly insane/numb" Yukio, despite everything, in chapter 93 kinda proved he still retained some "sanity/emotions" inside of him. After chapter 93, it'd look like he upgraded to a completely "insane/numb" state after all the shet that happens afterwards. But in chapter 97 I got some doubts.
In chapter 93 Yukio wonders "What is good and what is evil?" during his "raging/emotional rampage". And, finally, in chapter 97 he recognizes and defines Lucifer/Illuminati/their cause and he himself as EVIL. That's proof, to me, he's STILL sane, deep inside, or even just "rational" enough, despite everything. I see it as a sign of hope. A sign that he's still somehow on the same "level" of before chapter 93 even if it got "worse", on the other hand.
And if he really is, it makes me hope that another big/terrible/devastating revelation could still work on him as S13's did. What I mean is that I think that as long as he retains even a lil bit of emotions (even if he doesn' show them/he's not even aware of feeling them) there could be hope that by "provoking" them he could "snap" out of his "insane/numb" state again. (which reminds me of episode 24 of the anime with Rin saying "Yukio is still in there somewhere and if we keep calling him, he'll snap out of it.")
Back to chapter 93 again. After Yukio starts feeling "tired" he finds himself in front of Futsumaya, encounters Shiemi and talks with her. I like to think Yukio said those things/hugged Shiemi out of honest feelings. So, deep inside, as I think earthy said, Yukio craves affection but prolly just feels like he doesn't deserve it (or something along these lines).
Long story short, I feel Yukio is not completely that lost cause he seems right now. I don't know what exactly or what kind of "revelation" could make him "react" at this point and/or show signs of still being capable of feeling emotions but I'm kinda sure he still got 'em in him somewhere/somehow. Even towards Rin. And I'm not talking about "competition". He did say he loves and hates him and I like to count that as an "honest admission" as what he said to Shiemi.
Also, if Yukio recognizes himself (alongside Lucifer and his crew) as evil I wonder if he'll be willing to turn into an enemy/killer of humanity, after all, even if it's for his thirst of power. I believed it'd be prepared to do that if it wasn't for the fact he said/recognized he's evil. How could he prove he's "stronger" than Rin if he used his power to kill people? I think it'd be "logic" to use it to save them. Unless all Yukio is willing to gain power for is only to fight/defeat specifically Rin. But, I don't think so.
A couple last thoughts about chapter 97. When Yukio declares "I don't know what will happen if I go to the Illuminati blah blah" Yukio's pose and the fact he's covering his eye with his hand makes it possible to see very lil of his facial expression while he's saying those things. I wonder if that was on purpose. When Rin told Yukio "Someday I'm gonna surpass you", the panel (a pretty big one) was completely focused on him and his facial expression.
But in Yukio's case it's nothing like that. And considering the importance of the words spoken I expected more focus on this bit. Also, Yukio is looking at Rin while slightly turned to his left side. Why this choice? Wouldn't have given a "slightly" better view of Yukio's face if he was turned on his right side? Just technical stuff, forgive me.
Anyway, if the twins are gonna meet again only by the end of the manga, I expected a better "departure scene" with a better "stylistic structure". But as it's played/designed, it feels a lil "simplified". There could be reasons, but. And this connects to my second thought: at first I commented that I had a feeling the twins could meet up again only at the end. I read Yukio's words again. And he says: "But if we DO both live through this, I'll be stronger than you."
If I'm honest, at first I read it as: "Once all this will be over and IF we still will both be alive, we'll meet again and I'll be stronger than you." But, please, someone tell me this could be just my personal interpretation and what Yukio actually said can't necessary be read like this. I hope I'm wrong and that what Yukio meant is that the most important thing to him is that by the end of the story he'll be the stronger one so it's okay to him if he and Rin happened to meet once in a while and it's not like he wants/would run away if they happened to meet. 'Cause... I want to believe they will meet again sometimes and not in 10 years from now.
Edit:
It could a quick way to let them start a "rescue Yukio" mission. If they just start rescue right after Yukio's reveal, it would be too unrealistic like everyone is a saint, but now they have the information that Satan is between all these, so that will be enough reason. Since it doesn't seem like Yukio is completely forced to do so, they will know they have to be careful.
So maybe Rin will still be somewhat mad at Yukio the next time they meet, but it will be in a cool down state due to the complex situation.
For as much as I'd like the idea of Rin and co. going for another "rescue Yukio" mission, since the first attempt failed miserably and since Yukio made it plain clear he doesn't need help/can't stand to be rescued I kinda doubt this could happen again. If I'm realistic, I think even Rin would not take it into consideration now (for as much as he'd want to get Yukio back/have at least a chance to meet him/talk to him again). I think Yukio's point got through Rin for good after chapter 96.
I'm not saying Rin won't entartain the idea for a while (after he recovers) but I can already picture him replaying Yukio's words in his mind and think "Would it be a good idea to try and rescue him again after all?". If Rin still respects Yukio, I think he won't try to plan to rescue him again. But he won't also feel like letting him stay in the Illuminati. I guess he'll agonize over what to do for a while (always if, as I said, he'll be over his rage status toward Yukio after he'll have processed what happened).
Honestly, I don't know what he could come up with or what he could decide to do. Leave things as they are ("Yukio wants power and the Illuminati can help him? Then okay, I'll leave him be if that's what he wants.") or if he will still feel like not giving up on him. Or maybe things with the opening of the Arificial Gate will get worse and he'll be summoned to help and he won't have time/way to go for personal quests. If I got this right, involving Amaimon in the rescue plan, was meant to "save Rin and the exwires" by any "betrayal" accusation or something like this. So, technically, Rin and the exwires are "clear" and will still be considered members of the Order as if nothing happened.
Also, if Rin's gonna get some development by the end of this arc I suspect he may not be the "healdlong" guy as before who would just rush in to save someone. This is what I think. And the experience with Yukio may have him reconsider a lot of things about himself too.
So, I really have no clue. I only pictured a case were Rin and Yukio happen to meet and instead of offering him help, Rin offers Yukio to "use" him somehow, at least. Such as in the Aomori arc. At the time, Yukio studied a plan which involved having Rin stab Hachirotaro in the back in a surprise attack. So he kinda "used" him. Prolly Yukio is "okay" with this kinda "help". Just random thoughts.