Bibi may be a [insert derogatory descriptor here], but I do believe he believes in something bigger than himself and does care about his country. Chuck's just about personal money and power.
Perhaps, the point is that they can both sing nicely all the opposite tones. Pro Israel-anti Israel, pro charedim/anti charedim, so careless about Judaism/so passionate about Judaism. Don't fall for their b'ezras hashem and don't be so shocked that the "shomer" Israel is suddenly pandering to the anti Israel masses.