Do East Egg citizens see West Egg citizens as a danger? How do they react?
If we were to label the East Egg person as Tom Buchanan, and the West Egg person as Jay Gatsby, it might be easier to explain the possible feelings of the East Egg person towards the West Egg person.
The reason that Jay is a "danger" to Tom is because Tom was the one who was raised or "bred" to behave a certain way, yet Jay comes across as the true gentleman in the novel. Tom is obnoxious, he's rude, and he is even violent. He never has anything to do with his family (parents), he cheats on his wife, and he is not seen with his daughter except for in one scene. On another note, Tom is stingy with his money. He does not give one of his (many) cars to George, when it would have been so easy to do so.
Jay, on the other hand, is generous--he throws parties every weekend, he buys his father a house, and he helps to get Nick a job in the city. Jay is never rude--he is always quiet and is always a gentleman, even when Tom acts like a jerk.
These are the reasons why someone like Tom would feel threatened by someone like Jay. Tom knows he comes off like a jerk, but he doesn't care what others think. However, he wants to do all he can to belittle Jay and make him look like a criminal who never went all the way through his education at Oxford.