I would shorten your list and say Obama hates Israel because he IS a muslim.
I would quibble with that characterization, since in the United States, a person's religion isn't determined by law, but rather by what a person says he or she is.
The only downside to this is that an American is not only free to follow whatever faith he professes to practice or none at all, but is free to deceive others as to what his faith is. Most often, deceiving others about one's faith is harmless to the society as a whole. But when the electorate is choosing among political candidates, especially the President of the United States, it has a right to know the truth about about all candidates' religious preferences, because of the possible impact that might have on the candidate's policy positions.
Obama said and still says he's a Christian. Since he has lied about so many other aspects of his personal life, many doubt him on that. But still, out of respect for the American tradition of religious freedom, we have to accept him at his word - but only in so far as that issue is concerned.
It's still be possible for one to be a Christian yet have an unusual affinity for the Muslim world.