Religious liberty is protected in the United States by the First Amendment, which prohibits the Federal government from establishing a state church and restricting the free exercise of religion. However, I have seen discussion from people who resent that protection and want to minimize or eliminate it because they don't like what certain religious people and organizations are saying. In other words, religion is getting in the way of their secular agenda, and they would like it removed or at least stripped of any power to influence public policy.
I tried to make the case in my last post that everyone is religious in one form or another. Even if you don't like the term religious, I hope you will admit that you have some kind of an underlying world view, whether it is of a secular or religious nature, which affects the way you interpret events and make decisions. People who want to restrict religious liberty are in effect trying to force a particular world view on people, or render opposing world views ineffective. That is, they want to control the way someone thinks at a basic level, or if they can't do that, keep them from behaving in a way that is consistent with what they think.
I have heard people say, "it is fine for you to practice your religion, as long as you keep it in your church." This is like saying, "you are allowed to think however you like as long as you keep it to yourself and your small group of like-minded (and strange) friends."
Right now I'm reading Bonhoeffer - Pastor, Martyr, Prophet, Spy, by Eric Metaxas. Dietrich Bonhoeffer was a young German Lutheran pastor who was part of a conspiracy to assassinate Adolf Hitler. One of the last things Hitler did before his death was order the execution of Bonhoeffer before he could be liberated by the Allies. I'm about half-way through the book right now, and WWII has not yet started. However, early in the book we see that one of the first things the Nazis did as they were gaining power was infiltrate and control the German national church. Unlike the United States, Germany had a national church, and the Nazis recognized that they could have great influence on the thinking of the German people by controlling religion. This forced Bonhoeffer and certain other pastors into a situation where their practice of religion became illegal, and they were characterized as dangerous extremists.
The reason religious liberty is important is that it is fundamental to freedom of thought and expression. When the government or some power group is able to restrict religious practice, they are developing the ability to restrict any opposition and are thus becoming tyrannical.
Therefore, even those who do not consider themselves religious should still be supportive of religious liberty as an important part of a free society. If you don't like what certain religions say, you should engage them in discourse and debate rather than trying to silence and restrict them.