If I acknowledge that some communities are more likely to live their daily lives under these three factors altogether, it could explain why these communities may be more vulnerable to daily life challenges, and more easily resort to violence. Still, that doesn't give me a causal link between racial/cultural diversity and violence, far from it, but I can understand why those who prefer taking shortcuts may end up reaching this conclusion.
This shortcut is also very comfortable for the peace of mind: once I attribute violence to racial/cultural diversity, I can also safely conclude that I will never be part of the problem (if I consider myself as being part of the "good" racial/cultural group)...