Islam is a religion. Islamic republicanism or Islamism is an ideology. My brother has read the Koran. Unlike the Bible, which contains many archaic laws, it is possible to rigidly apply the Koran to one's life, so it's all or nothing basically. It is also a very well-written book, according to my brother. It's so persuasive, in fact, that he wouldn't drink or eat pork (and we're FRENCH, we love our andouillettes and our saucisson and our wine lol!) until the effect of the Koran wore off.
So, yes it is a religion, but not a religion of peace. Mohammad was a warrior who tried to convert 200 Jews in Mecca. 199 of them quietly muttered Hebrew prayers while in line to get their heads chopped off. End of story.
Islam is both a religion and the legal system in one all encompassing whole.
The "Bible" can either mean religious system of ancient laws and rituals based on Old Testament which requires continuous interpretation and adaptation or if sumplemented by New Testament it lays fundation for spiritualized non legalistic way of life.
The first choice gives you Talmudic Judaism, the second gives you Christianity. Only Christianity allows for the real separation of secular and religious spheres.