Israel is not a democracy like ours.
True. Israel is a Parliamentary Democracy, where the Executive Branch is not distinct from the Legislative.
America is a Constiutional Republic, with a Separation of Powers between the three branches, Executive, Legislative, and Judicial. And our Legislative Branch is Representative, not Parliamentary.
A man who calls others lice would not be in our Cabinet. He wants to deport Israeli citizens because he doesn't like their ethnic group. His being in the Cabinet shows that they don't share our values.
I don't think you've accurately represented Ze'evi's views here, but that's beside the point. In a Parliamentary Democracy, unless one party wins a solid majority of the legislature, they need a political coalition in order to form an Executive government. The price for bringing smaller parties into the coalition is often giving them a lesser cabinet position. This is what Sharon did when he made Ze'evi Minister of Tourism.