The Islamic Republic of Iran, as it calls itself, is not a republic, but it is Islamic.
Here are two definitions to make the point before moving on to a larger point.
A republic is defined by dictionary.com as “a state in which the supreme power rests in the body of citizens entitled to vote and is exercised by representatives chosen directly or indirectly by them.” Iran’s elections put supreme power in religious leaders, not the people. In previous elections when there were public demonstrations in opposition to the government, “the people” were jailed, or murdered by the regime.
Radical Islam is a system of beliefs founded on interpretations of the Koran made by political leadership that seeks to impose those beliefs on its citizens and the rest of the world, by force if necessary. At least that’s my definition, based on sermons from hardline mullahs in Iran and elsewhere, along with personal observations about how those beliefs are put into practice.
Obviously not all Muslims agree on everything, especially when it comes to politics. Neither do Christians and Jews, but Christians and Jews are not known for wanting to eliminate nations they don’t like or for forcibly imposing their will on others.