The debate over separating church and state often proceeds as if there were only two sides - those who favor it and those who oppose it. In reality the debate involves quite a bit more nuance than this, with a broad spectrum of possible positions: strict separation, accommodation, non-preferentialism, and theocracy. The idea of supporters and opponents is a simplification which is often sufficient, but a proper understanding of the issues requires familiarity with the different positions from strict separation to outright theocracy.
As a general rule, separationists are those who support the separation between church and state. The level of support will vary, however. The strictest of separationists advocate separation in every way and on every level. They deny that the federal government has absolutely any power over religion whatsoever, and as a consequence, they argue that the government should not have any involvement with religious organizations whatsoever.
The accommodationist approach to the separation of church and state opposes the separationist approach which has been dominant in the courts. According to
accommodationists, the First Amendment should be read much more narrowly than it has been in recent years. Some go so far as to argue that the First Amendment prohibits the government from doing nothing other than creating a
National Church — everything else is permitted.
In the debate about the separation of church and state, the perspective known as non-preferentialism is best understood as a subset of accomodationism. Like accommodationists, the non-preferentialists also oppose the recent legal trend which has emphasized stricter separation, and advocate instead a closer relationship between religious groups and the government.
The most extreme position opposed to church/state separation in all of its forms is held by those who can be called “theocrats,” these are people who wish to create a theocratic government in the United States. To state it plainly, the theocrats consider even the most conservative Christians in the Religious Right to not be “godly” enough. Sometimes arguing that a theocracy was intended for the United States from the very beginning, theocrats believe that any sort of compromise would be invalid.