The GOP exploits terrorism because the GOP is and always has been bankrupt morally and intellectually. A rich party monetarily, the GOP is utterly bereft of ideas or hope. The GOP encouraged fear of communism and was, arguably, it's sole beneficiary. Even so, the GOP, increasingly radical under Ronald Reagan, raised other bogey men: drugs, porn and terrorism.
GOP efforts against porn and drugs would fail, it's own membership being among the worst offenders. With the collapse of the 'Soviet Union', the GOP would be left with a single bogey man: terrorism!