The very idea of separating church and state continues to be controversial, despite how well it has worked for churches, governments, and citizens over so many years. Opponents of church/state separation are able to manufacture and prmote controversy by promoting misunderstandings about what church/state separation really means and what it does. The more you understand church/state separation and secularism, the easier it will be to defend it against attack from theocrats.
That is true, the phrase "separation of church and state" does not actually appear anywhere in the Constitution. There is a problem, however, in that some people draw incorrect conclusions from this fact. The absence of this phrase does not mean that it is an invalid concept or that it cannot be used as a legal or judicial principle.
This claim is common, but it rests on a misunderstanding of what real freedom of religion entails. The most important thing to remember is that freedom of religion, if it is going to apply to everyone, also requires freedom from religion. Why is that? You do not truly have the freedom to practice your religious beliefs if you are also required to adhere to any of the religious beliefs or rules of other religions.
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.