What does it mean to be 'free' in a liberal democracy? At the very least, it must mean that people are able to form opinions and pursue goals relating to the direction of their life with a minimum of interference from the state. If people are prevented from developing their own ideas about what constitutes a good and moral life, they simply become tools of the state. This is especially true when the state promotes the ideology of any one religion as defining what is good and moral.
This is very important for atheists who wish to live their lives free of any interference from religious leaders or institutions which want to impose on others some particular theistic conception of what is good. Religious citizens can choose to accept an alleged god's alleged commands about what constitutes morality, but neither atheists nor theists can have such commands imposed on them without thereby undermining the very principles of a free, liberal democracy.
In Justice as Fairness: A Restatement, John Rawls writes:
[C]itizens are free in that they conceive of themselves and of one another as having the moral power to have a conception of the good. This is not to say that, as part of their political conception, they view themselves as inevitably tied to the pursuit of the particular conception of the good which they affirm at any given time. Rather, as citizens, they are seen as capable of revising and changing this conception on reasonable and rational grounds, and they may do this if they so desire.
As free persons, citizens claim the right to view their persons as independent from and not identified with any particular conception of the good, or scheme of final ends. Given their moral power to form, to revise, and rationally to pursue a conception of the good, their public or legal identity as free persons is not affected by changes over time in their determinate conception of the good.
All of this, naturally, relates to religion and the state's relationship with religion:
For example, when citizens convert from one religion to another, or no longer affirm an established religious faith, they do not cease to be, for questions of political justice, the same persons they were before. There is no loss of what we may call their public, or legal, identity — their identity as a matter of basic law. In general, they still have the same basic rights and duties, they own the same property and can make the same claims as before, except insofar as these claims were connected with their previous religious affiliation.
We can imagine a society (indeed history offers numerous examples) in which basic rights and recognized claims depend on religious affiliation and social class. Such a society has a different political conception of the person. It may not have a conception of citizenship at all; for this conception, as we are using it, goes with the conception of society as a fair system of cooperation for reciprocal advantage between free and equal citizens.
In a liberal democracy which promotes liberty and freedom, a person's status as Catholic rather than Jew, or Hindu rather than Muslim can have absolutely no bearing on how they are treated or viewed by the state. Jews and Muslims, Catholics and Hindus should all be treated in exactly the same way; thus, someone's conversion from one to the other — or to nothing at all — must have absolutely no impact on their status in the political community.
This, however, is precisely what is under assault by those who seek to undermine the separation of church and state in America. They would make religious beliefs — and therefore religious affiliation — relevant in political contexts. Political citizenship would be experienced much differently between Catholics and Hindus because belonging to one religion rather than the other would produce extra privileges.
The very act of calling America a "Christian Nation," for example, is at a bare minimum a symbolic attempt to describe America in Christian rather than secular terms. A "Christian" nation is one in which the Christian beliefs of people or institutions become relevant to their status in the political community. We would not all be equally "citizens," but first and foremost "Christian" as defined by the state or "not Christian" — and thus politically inferior.
This, then, means that the assaults on the separation of church and state are, in the end, also assaults on not only liberty and freedom, but also on the very concept of citizenship in a liberal democracy.
