A good example of someone advocating this idea can be found in a letter written by Emily Marino to The Day:
[T]he First Amendment originally was intended to protect the church from the state and not the other way around. The reason the Pilgrims and many others fled England was because they wanted freedom in how they worshiped God, not which god they did or didn't worship.
There are a number of problems with this position. For one thing, it's simply incoherent - separation can't operate "one way." You can't have religion interfering with government without government returning the favor. For another, the argument above presumes that there is such a thing as "the church" - but that abstraction doesn't exist.
In reality, there are many churches, many denominations, and many religions. If the government is protected from "the church," which "church" would that be? If only one (and people often assume their version of Christianity here), then that discriminates against all other groups. If all groups are included, then what you have are multiple organizations competing for government largesse on the basis for religion - but religion isn't supposed to become the basis of political division and strife.
That's exactly what the First Amendment is suppose to prevent, and why it also protects the government from religion. If people don't have freedom in what god they worship, if any god at all, then the country isn't religiously free.