Yes, the Jump SQ poster puts their allegiance quite interestingly. For Yukio, Order is evil, he only knows what was on the drive. Lucifer made known his intentions to kill everyone, so that is evil as well. So he most probably would keep improvising his plans until he finds what he needs. His fight against Rin is something I am looking forward to but Lucifer might not want any harm coming to Rin for Satan's sake except for getting him as vessel. Maybe Satan makes his move once Yukio confronts Rin? And with Todo, it would be interesting to know where it leads. I wonder if Todo family having white hair is due to Azazel heritage. They are reputed for maintaining deepkeep.
You know, the order may have done quite a few evil things but it is nowhere near the level of evil that the illuminati is. The illuminati is basically a death cult with zero redeeming values doing the bidding of an angsty demon king who is too hung up on the world being unfair to him, while the order still cares for humanity and all the evil things it did in the first place is either being done by a rogue faction that does not share the views of the rest of the order or was done because Lucifer was threatening to self destruct and take the entire world with him. So even the evil things done by the order can mostly be blamed on the leader of the illuminati. There is no way yukio can see the order as a greater evil, especially given his family and friends are still with the order and deep inside all the hatred and jealousy he still must have some care for them.
The Todou family has white hair? I thought Saburota had black or brown hair and Homura has black or brown hair with with one yellow stripe. Even then, I don't think white hair equals Azazel ancestry as Mamushi and her sisters also have white hair and I am certain they don't have Azazel's blood in them.
Renzou has been a spy for Mephisto, Lucifer, Lightning and the man in the shadows. Double spy is an understatement. Right now, he might be the one with most information about the ongoing. It would be interesting once he returns back to his family and the Order that is if he has a chance to. There is another bit about the one who actually recruited him. Maybe we have another spy already working with Illuminati.
Renzo is still just a double spy. Mephisto and Lightning both work for the order, while the man in shadows seems to be an illuminati agent as it is confirmed that they sent him to pressure yukio to defect. Also doing one favour for lightning so that he will remove the sylph bell does not equal to being a spy for him. As of now, unless the shima family are shown to have their own motivations separate from the order, the illuminati and order are the only factions he spies for.
Also I think it is all but confirmed that Homura Todo recruited him as he already mentioned that it was a different Todou that approached him and in the flash back he stated that it was a young woman who gave him a card of the illuminati. I think the only thing that is left regarding his recruitment is whether Renzo really did join the illuminati for the shallow reason of having some fun or is there some deeper meaning behind those reasons and/or deeper motivations. Not to mention his whole "deceiving the people I love is my specialty" line which does seem to imply that he has been lying to his friends and family even before becoming a spy.
I also noticed that we see an affiliation between the brothers with the Myodha. While Rin has close connection to Suguro's family, Yukio has similar closeness with Shima's. And if the Salaryman Exorcist is any hint, Konekomaru is close to Yukio as well.
I don't think there is much of an affiliation between the brothers with the Myoudha really. Tatsuma is like a father figure to Rin thanks to his relationship with Shiro but Yukio's relationship to Shima family seems purely professional since they are for all intents the representatives of the Myoo dha sect (since if I remember correctly Tatsuma has not joined the order) in the order and Yukio's superiors so he has to report to them. Not to mention the Shima family is subordinate to the Suguro family and clearly very loyal to Tatsuma and Ryuji given how they treat Ryuuji as a more valuable family member than they ever treat Renzo who is supposed to be part of their actual family. Although I do feel Juzo and Yukio's tag team against Todou might see a repeat with Renzo and Yukio fighting against Todou in a similar fashion in a future battle. Tatsuma and the Myoo dha are still researching a way to separate Karura from Saburota so I am guessing a future conflict between the Myoo dha and Todou is inevitable.
As for the Salaryman manga, I don't think it is canon. And even in the main series, Konekomaru clearly has a much deeper bond with Rin than Yukio.
Illuminati arc is going to go on at least until we have some hint that 'all eyes would be one, no human no demon'. I mean that artificial Gehenna gate is opened enough to force bigger changes or that Mephisto is able to freeze the gate back again. Then there is Shiemihaza arc running concurrently with what is going on in KRC lab with Drac. Rin might get a hint of something important in the past that might help him control himself or fight Illuminati.
Does Rin really need any hint from the past to help fight the illuminati? The only problem in the illuminati is Lucifer and honestly if there was anything in the past that could be key in combating Lucifer, I am pretty sure Mephisto would know, and given how much he trembles at the sight of Lucifer even now, I don't think he would waste time when it comes to teaching Rin a way to kill Lucifer.
Also wasn't there being a flashback of Yukio where Shiro told a younger him that there will come a time when he has to save his brother? Given that we have seen demon Rin now, perhaps Rin's demonic side will overpower him causing Yukio to save him from said demonic side and bring him back.(or perhaps the order will see Rin's evil demonic side and decide to execute him anyway causing Yukio to save him as this time he is no longer a part of the order and thus will have no reason to care about breaking the rules anymore). Either way, Yukio having a proper fight with his brother where both can vent their frustations with each other, and actually getting the chance to properly save him might do a great deal to resolve the many issues he has with his brother and himself.