Shima and Yukio... They've got a great contrast. Shima has always been a laissez-faire kind of guy, letting stuff happen. Contrast Yukio, who always keeps himself under lockdown for fear of getting bullied. Shima's already in the Illuminati, and circumstances are pushing Yukio towards the Illuminati.
Honestly, I don't think it's crossed Yukio's mind yet how to think of him. It's a big embarrassment as a teacher to have a student turn out to be a spy for the evil organization. But Yukio doesn't exactly value being a teacher more than the title. He's shown little to no emotional connection to any of his students in classroom (Rin and Shiemi exempted). He stays professional and aloof. I think he just has decided that Shima is just another enemy to take down.
But if they did end up in the Illuminati working together, I think Yukio would be very critical of Renzou. Yukio is utterly obsessive when he does something. As an exorcist of the Order, he holds himself to a high professional standard and a very narrow viewpoint. I would think that as a valued member of the Illuminati, he might loosen up a little but would still throw himself into the job. Shima seems like the type to start drifting away from the job as he realizes it wasn't what he wanted it to be. I think Yukio would not be able to stand this attitude, especially from a colleague he'd have to work with.
I think Renzou would also be ticked with Yukio, as Yukio has similar unyielding dedication to Renzou's brothers.
Augh, I miss being able to write fanfic. I have no time in life now. Wagh!