I've never met any of the home world gems except for one, and even she had been imprisoned on Earth for many years, so its not accurate.

The Crystal gems have been on Earth a long time, and they fight to save humans. They're a little rough around the edges, but they're very knowledgeable and kind and have the best interests of Earth at heart. The home world gems, they have their own agenda, and from what their actions have been so far, I would say they're not very concerned toward earth's inhabitants.