That is in effect, true.
There is no practical means to ensure an amoral position in this government or any other single thing. There is no "moral-neutral" position or any position outside the bounds of morality (whenever morality is concerned), as any position is a moral position by it's nature.
Hence "amorality" is a fallacy for all practical purposes except as a means of definition. The only real control is in whose morality one or all must embrace.
How then may one form a secular view (not to mention govt) when one cannot exist?
We have never been secular, only tolerant. Historically, all of our laws have necessarily been viewed through the prism of the Judeo-Christian ethic.
The only way to change that is to substitute another moral code, as the socialist left is trying to do. Secularism as well as multi-culturalism are simply means to their predictable end: Socialism/Communism.
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If we can believe the writings of people like Joseph Story on the subject, it was intended that such control be forever excluded from the powers exercised by the federal government, and to the extent that it is exercised it be the exclusive domain of the States. The argument seems calculated to render that an impossibility.