Myth:
This "separation of church and state" is anti-religion.
Response:
One tactic against church/state separation is to portray separation as anti-religious. Because the American government cannot be hostile towards religion, it is argued that church/state separation is an illegitimate infringement on citizens' religious liberties. Their "solution" to what is really a non-existent problem is to mingle religion with government, thus promoting theocratic systems as if that could enhance religious liberty instead of, as is actually the case, undermine it.
Trivializing Religion
What many forget is that the separation of church and state not only protects the state, but also protects their religion from government interference. And, just as importantly, it protects religion from being made trite and irrelevant by virtue of its involvement with the state. The state is not permitted to promote particular religious doctrines as religious doctrines, that much is clear, but in the attempt to do it anyway, some really poor rationalizations are used. The most common is that we aren't really dealing with "religion" anymore and that the doctrine, symbol, or words have magically become "secular" over the course of time.
But do devout Christians really want their holidays, their religious symbols and quotes from their savior, Jesus Christ, treated by the state as irreligious, secular components of society? Does that really make any sense at all? There are two choices: argue that these religious symbols and words are secular in order to get government endorsement, or reject government endorsement in order to preserve their religious nature. Truly devout believers can only justify the latter option which raises questions about the true motivation of those who follow the first choice.
Protecting Religion
Throughout American history, many Christians have recognized that the separation of church and state protects Christianity as well as other religious faiths. Roger Williams, for example, argued very explicitly that in order to try and keep the Church pure from the influences of evil, it is necessary to keep it separated from civil government. More than that, however, he also thought it was important for the state that it, too, be kept separate from the workings of the church:
Magistrates [officials of the civil government] have no power of setting up the form of Church Government, electing Church officers, punishing with Church censures, but to see that the Church does her duty herein. ...
And on the other side, the Churches as Churches, (though as members of the Commonwealth they may have power) have no power of erecting or altering forms of civil government, electing of civil officers, inflicting Civil punishments (no not on persons excommunicated) as by deposing Magistrates from their Civil Authority, or withdrawing the hearts of the people against them, to their laws, no more than to discharge wives, or children, or servants, from due obedience to their husbands, parents, or masters; or by taking up arms against their Magistrates, though he persecute them for conscience.
- Roger Williams, Bloudy Tenent of Persecution for Cause of Conscience (1644)
James Madison expressed a similar sentiment when he said "Religion flourishes in greater purity without than with the aid of government." In a letter from 1819, he further noted that "the number, the industry and the morality of the priesthood, and the devotion of the people have been manifestly increased by the total separation of the church and state." In neither case were these men expressing a position which was anti-religion. On the contrary, they both believed that religion is important to people and wanted to ensure that it would be able to continue doing good by separating it from the power of the state.
Church/State Separation & Religious Diversity
It is important to keep in mind the fact that the United States is a country where religious belief and religious diversity are usually greater than in most other places. In countries where there is an established church and/or official state support for religion, both belief and diversity tend to be at least a little bit lower, but sometimes a great deal lower.
So if it really were true that the separation of church and state is anti-religion, it would have to be argued that religion has flourished here more than elsewhere in spite of separation rather than because of it. Maybe someone could make such an argument, but I doubt it I have yet to see anyone actually make a case for that, but it is quite common to find people arguing that church/state separation has encouraged religious diversity.
This may be why books and articles attacking church/state separation normally ignore this issue and only focus on a few incidents where Christians have had problems due to separation claims. It's probably not a coincidence that those who benefit most from an environment which encourages religious diversity are non-mainstream Christians and non-Christian religious minorities while those complaining about the alleged anti-religious nature of separation are members of mainstream, privileged Christian groups.
Church/State Separation is Anti-Privilege
Now we have a hint about where the complaint about separation being anti-religion is really coming from: it is, in fact, anti-privilege in the sense of opposing special privileges for particular religious groups, religious traditions, religious beliefs, or religious believers. Members of traditionally privileged groups may perceive separation as anti-religion because it denies them privileges which they may have come to expect.
It's not really anti-religion because it ensures that all religions and all religious believers are treated equally. Those who are used to and who expect to be privileged, though, may not care so much about whether others are being discriminated against or relegate to a second-class status. They only see their own loss of status, not others' gains in equality, and this loss of status is generalized to religion overall.

