So basically Daidai is the anti-Yume: by having an absolutely empty cranium and never attempting to "understand anything" (the opposite of omniscience), she becomes impervious to any and all danger especially gray-related ones without having to even make an effort to avoid them. There is a fascinating implication here. Since Yume no longer has omniscience, she cannot just "know" that a gray job will have some Lovecraftian being messing around, so she readily accepts the jobs. But once on-site, the remnants of her power activates and she can perceive them faintly, narrowly avoiding the full brunt of the gray's influence each time and surviving. What this means IMO is that a gray's influence on you is mainly related to the act of observing it and understanding what it is.
Not observing it/be outside of its immediate area of influence - you're basically immune
Observing it but not giving a shit because you don't understand it and hence don't know that it's dangerous - still immune and can even interact with them freely (Daidai is here)
Recognizing signs that it is there, and your instincts tell you it's deadly - the gray can kind of affect you but you can still take measures to evade it (Yume is here)
Fully observing it, realizing what it is and what it can do, which breaks your mind - you are dead, or at least go insane (most of the victims in this manga are here)