Absolutely not. While the separationist community includes many people who are non-religious, the majority of separationists are members of religious communities. There is good reason for this; separationism was created to protect religious rights, and has had the effect of preserving the influence of religion in America. A brief look at the history of America suggests just these conclusions.
On any reckoning of the evidence, separation of church and state has characterized the life of our country. In contrast to other Western nations, Americans have never been expected to adhere to a national religion or support a national clergy. The few state establishments that existed after the adoption of the Constitution faded of their own accord in the early 1800s. Despite widespread prejudice against non-Protestant and non-Christian religions, religious minorities have had remarkable freedom to proselytize and worship. For over a hundred years our public institutions (libraries, schools, and universities) have been predominantly secular. Yet separation has had none of the negative side effects that its detractors have feared: Americans remain overwhelmingly religious; their religion retains a vitality and cultural importance that is unparalleled in the industrial West; religious leaders are free to comment on political matters and to counsel their flocks on matters of public importance. Indeed, as we write these words, our country is in the midst of a two-decades long revival that has changed our politics, our culture, and our national identity. There is nothing in this record, in other words, to suggest that separation has weakened our religious faith. If anything, it has spared our country the religious infighting that has characterized the history of so much of the rest of the civilized world.
The conclusion, we suggest, is obvious: separation of church and state is good for religion. When religion is propped up by the state (as, for example, in most of Western Europe) people loose their initiative and passion (eg., only a tiny percentage of Western Europeans are actively involved in religion, despite the widespread existence of state supported churches). Conversely, when the state uses its power to suppress religion generally (as, for example, in Eastern Europe), or particularly (as, for example, in Africa and the Middle East), it results in social unrest, civil war, and religious genocide (eg., Bosnia and Angola). The best policy, in our view, is one that allows religion to flourish on its own merits, free from coercion or support from the state. Indeed, this is exactly what Thomas Jefferson, one of the greatest American defenders of religious liberty, believed.
As to American religious institutions, we note that the vast majority of them are separationist. Virtually all mainline Protestant denominations are separationist (the most important exception being the Southern Baptists, who reversed their historic support for separation in the wake of a conservative takeover of the denomination in the 1980s). Reform and Conservative Jews are separationist, as are most of the Non-Western religions that have found a home in this country (Islam, Hinduism, Buddhism, etc.). In practice, opposition to church/state separation seems confined mostly to conservative, evangelical Protestants and (on some issues--especially school vouchers) Roman Catholics. No one doubts that many religious people are opposed to separation, but many more favor it, and the weight of history is on their side.
Finally, we note that even those who see themselves as opponents of church/state separation agree that the Constitution limits the power of government to legislate about religion. Rather, the contemporary debate revolves around the degree to which the Constitution separates church and state. Our opponents in this page--religious conservatives who have bought into the political philosophy of accomodationism--argue that the Constitution allows government substantial room to meddle in the religious affairs of the individual. We think the accomodationists are dead wrong. We believe that if accomodationists paid attention to the history of our country, they would realize how dangerous their position is, both to their own freedoms and to the freedoms of others.