How has the hatred generated by the Arab refugees been politically exploited and how has it affected the state of Israel?
Both hatred and fear have been exploited politically for half a century or more between these two peoples by their elected leaders and by the armed extremist groups in each camp. The main tactic, and this goes both ways, is that people who are afraid or angry want someone to fear or blame, so politicians provide the scapegoat for whatever the current ill is: poverty, terrorist attacks, discrimination, border issues, and past conflicts. In this way the politicians benefit in two directions: they aren't blamed for any current problems, and they get more votes because of people's charged emotions.
This goes both ways, Israeli and Palestinian, and is not unique to these two countries (see: Cold War, U.S.).
It affects Israel in a couple of immediate and long term ways that I can see. First, it limits the individual freedoms of Israelis as they are more willing to surrender civil liberties when they feel threatened, and it forces the state to spend more on policing and the military than perhaps it needs to, as politicians must show they are serious about fighting the threat, even if it's not as serious as they sometimes make it out to be.
Great question by the way.