This woman getting caned in public is a violation of human rights. While I feel the government should allow people to practice whatever religion they want, a line has to be drawn when a woman is getting caned in public for something so trivial. When human rights are involved, then yes, I think the government should step in.
The government has a duty to protect and provide for its citizens. This includes creating laws that determine what is right an what is wrong and enforcing them. Some aspects of what is morally right and wrong impinge on other people's rights and when it does this then government has a right to enforce its laws. In the case of the Indonesian woman, no case can justly be made for an act that adversely affects another party. The laws of morality must be objectively determined via a transcendent agent.
No, governments should not be involved in the morals of people. This 20-year-old woman was just standing close to her boyfriend and she was beaten with a cane. That is punishment for something that is innocent and natural. What kind of government sanctions that kind of behavior? Governments have no right to be involved in the personal lives of people.
Government should be the promotion of a public good. And because different people have different morals, the government cannot impose a single morality that agrees with all its people. Government should be subject to the people, not the other way around. A government that punishes immorality suppresses its people not promotes them.