Dear 100 Hour Board,
Why are some praying mantises green and others are brown?
This article has a pretty good summary of a paper called "Colour Change and Habitat Preferences in Mantis Religiosa" which gives a pretty good answer to your question. It turns out that praying mantises can actually change colors! The authors of the paper Battiston and Fontana found more brown praying mantises during the summer when the vegetation was more dry and brown, and they found more green praying mantises in the autumn after it had rained. This helps the mantises blend in with their surroundings and avoid predators.
They also raised some praying mantises in a lab where they were surrounded by abnormal colors (pink and blue) and they were safe from predators. However, they were still exposed to natural sunlight. Even though there weren't any predators and their surroundings didn't change from brown to green, these praying mantises still changed from brown to green. However, the change was slower and incomplete, so the researchers concluded that praying mantises change colors in response to some combination of climate, surrounding vegetation color, and the presence of predators.