1) They are not holding Christians in jail to make them forsake their beliefs. There is no attempt to make anyone forsake their beliefs. There is no one who is in jail because they are a Christian.
2) They are holding a public governmental official in jail for defying a court order. The charge is contempt of court. Any public official who defies a court order can be put into jail. This is the only reason that this woman was in jail.
3) They are not putting anyone in jail "for the rest of her life". In fact, she is currently out of jail.
4) Name a public figure who has not had "hateful statement" directed at them. Many public figures have had people say mean things about them without failing to keep their oath of office or keeping fellow Americans from getting married.
5) The prominent gay rights activists have been persistent, but they have been far from hateful. Many if not most were arguing against this lady being held in jail.
6) Putting people in jail based on "contempt of court" is not only effective, it is appropriate. This is the way that judges ensure that the authority is respected. People can't be allowed to defy the direct lawful order of a judge.
7) This woman has stated she is acting by the authority of God. As a public official who has sworn to uphold the laws and the Constitution of her state and country, this is bogus. She is breaking her oath of office. She deserves the consequence. God has no say in this.