GMO said: Actually, by the time they've beaten each other up to no end, they'll get along just fine, enough to a make tag team against their most hated enemy.
Well I don't know anything about Shizuo but I do know that Mokou has one thing going for her. She is Immortal.
Shizuo is immortal too. Well not really, he's just got super strength from drinking milk and being able to access unfathomable bursts of bodily adrenaline whenever he gets upset. Doing so, crushing his body and bones to the point where they were indestructible.
Out of all people, those two would certainly not fight with each other, but would rather be great friends. They do share quite similar values and thought process.