This "separation of church and state" is a communist plot.
Arguing that the concept of a "separation of church and state" is an attempt by communists to control the United States used to be more common during the Cold War, but it still gets trotted out occasionally by opponents to church/state separation. As with other things labeled "communist," this is more an attempt to discredit through association than any serious critique of separation, it's merits, or its actual history. In reality, church/state separation is very, very American.
The earliest known advocacy for a separation of church and state comes from the followers of Faustus Socinus (1539-c.1600), a religious reformer who was born in Italy but who later moved to Poland because it was a safer place for unorthodox thinkers. The works of his followers would later influence John Locke's writings on religious toleration and Locke's writings about liberty generally, not just religion, were very influential with the founders of America.
Church/State Separation in North America
The earliest person in North America to advocate a separation of church and state appears to have been Roger Williams, a religious reformer who founded not only the first Baptist Church on this continent, but also the colony of Rhode Island where he hoped to find greater religious freedom than among the Puritans he left behind in Boston. Contrary to what many believe, we even owe to him the words "wall of separation," rather than to Thomas Jefferson:
When they [the Church] have opened a gap in the hedge or wall of separation between the garden of the church and the wilderness of the world, God hath ever broke down the wall itself, removed the Candlestick, etc., and made His Garden a wilderness as it is this day. And that therefore if He will ever please to restore His garden and Paradise again, it must of necessity be walled in peculiarly unto Himself from the world, and all that be saved out of the world are to be transplanted out of the wilderness of the World. ("Mr. Cotton's Letter Lately Printed, Examined and Answered," The Complete Writings of Roger Williams, Volume 1, page 108 (1644))
Williams argues that, when the separation between church and state is breached by the church, then the church itself suffers. Instead of a garden, it becomes an uncivilized wilderness, plagued by weeds and undergrowth. It is likely that Williams is referencing a parable in Matthew:
He put before them another parable: "The kingdom of heaven may be compared to someone who sowed good seed in his field; but while everybody was asleep, an enemy came and sowed weeds among the wheat, and then went away. So when the plants came up and bore grain, then the weeds appeared as well. ...
The one who sows the good seed is the Son of Man; the field is the world, and the good seed are the children of the kingdom; the weeds are the children of the evil one, and the enemy who sowed them is the devil; the harvest is the end of the age, and the reapers are angels..." (Matthew 13:24-39)
Even as early as 1644, then, people recognized that a "wall of separation" between the church and the state was not a wall which only worked "one way." Instead, it was something which should protect both church and state from each other, ensuring that both could fulfill their functions properly.
Church/State Separation & Communism
Now, regarding the "communist plot" theory, it is true that Article 124 of the Soviet Union's 1947 constitution can be translated to include the concept of a separation of church and state:
In order to ensure to citizens freedom of conscience, the church in the USSR is separated from the state, and the school from the church. Freedom of religious worship and freedom of anti-religious propaganda is recognized for all citizens.
So, at least on a formal level, the Soviet Union guaranteed church/state separation, but does this mean that church/state separation in America is really a communist plot? Of course not. It's plain that the Soviet Union also equally guaranteed "freedom of conscience" and "freedom of religious worship," but how many Christians would argue that religious liberty is actually a communist plot? I doubt that any would at all, not even those who actually oppose religious liberty because they would prefer a theocracy.
The truth is that something doesn't become a "communist plot" or even just "communist" in nature simply because a communist country happens to provide it or guarantee it. The concept of church/state separation existed in North America three hundred years before the above was written and another 50 years before that in Europe. To label calls for a separation of church and state as some sort of "communist plot" requires a grotesque ignorance or distortion of history.