Normally they will in cases where the law is clearly being broken. However note that it is not a good practice to go against the actions of your own followers. I know that my denomination attempts to stay clear of these types of organized events. I was taught in school that if you stray to far from what the Bible says to concentrate on...you just become another voice in the crowd of voices. In church speak if you get too far from preaching Jesus....you are too far from the mission of the church to be effective. IE: Keep your sermons out of politics and political hotbed issues.
More than the government acting on this, it would be refreshing to see these citizens and the religious institutions behind them questioning their own actions.