Do religious beliefs and laws work together?

They can. In most Islamic Republics, the law of the land is the Koran, and so there would rarely be any conflict between religious belief and the law. In other places there may be some conflict, but these conflicts should be workable. For example in the US people are free to practice religion and to observe any laws connected with religion as long as they do not violate the civil law in the process. Many practice the Jewish dietary laws and no one is going to suggest that there is any problem with the civil law. Catholics must receive communion at least once a year in order to remain Catholics, and civil authorities are not going to prevent someone from obeying that law. If a religious law required that someone be severely beaten, or kept prisoner in his/her own home, then the civil law would have to step in. In the US, everyone's right to practice religion freely is protected by the fact that there is one law, the civil law that comes from the People's adherence to the Constitution. While there may be some examples where the Constitution and local law would trump religious law, it is all part of the greater good and the greatest protection of everyone's basic rights.