Do Americans hate British people?

I live in both Britain and America. However, as I have a British accent, Americans insult me frivolously. They think I'm some posh fart, and how many blasted times have I heard "Do you eat crumpets, maybe you should go drink tea, pip pip cheerio." The first two phrases are annoying enough, pip pip cheerio really pisses me off. I have never said pip pip cheerio in my entire life. They also call Britain a socialist country, which also pisses me off, since that's baseless rubbish. "Go play cricket, Brit", "If it weren't for us in World War II". What the hell is wrong with you Yanks?