Liberals hate Bush because he was particularly bad even for a Republican. He's a war criminal who started a war for no good reason.
Republicans hate Obama like they would hate any generic Democrat. The conspiracy theories they believe about him may be tailored to his particular race but they will believing similar ridiculous things about the next Democratic president.
Question (I'm legitimately curious):
Would you have the same impression of why conservatives dislike him if he were the same President and race, but his name was Barry Smith?