You've conveniently ignored the Establishment Clause.
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
The reason is so that the free exercise of religion is not interfered with by the state ...
That is Free Exercise Clause, not the Establishment Clause.
What does the Establishment Clause mean, rand?
... not that anti-religionists could create a doctrine that science cannot include religion ...
Science does not include religion. Period.
... so ban thought in the class-room if it relates to religion.
Thought is not banned.
How would one ban thought if one were inclined to do so? Install a really big fMRI in the classroom, point it at one student at a time, analyze their thoughts and banish those who were thinking of a god?
The establishment clause has the same purpose, to protect religion and religious speech.
The establishment clause has generally been interpreted to prohibit:
1) the establishment of a national religion by Congress, or
2) the preference of one religion over another or the support of a religious idea with no identifiable secular purpose.
At an absolute minimum, the Establishment Clause was intended to prohibit the federal government from declaring and financially supporting a national religion, such as existed in many other countries at the time of the nation's founding.
Thomas Jefferson wrote a letter to the Danbury Baptist Association in 1802 ... The letter contains the phrase "wall of separation between church and state," which lead to the short-hand for the Establishment Clause that we use today: "Separation of church and state."
The Establishment Clause has been interpreted to mean that the state can't do anything that "aid(s) or prefer(s)" any religion:
It is one of the fundamental principles of the Supreme Court's Establishment Clause jurisprudence that the Constitution forbids not only state practices that "aid one religion . . . or prefer one religion over another," but also those practices that "aid all religions" and thus endorse or prefer religion over nonreligion. Everson, 330 U.S. at 15. See Wallace v. Jaffree, 472 U.S. 38, 53 (1985)("[T]he individual freedom of conscience protected by the First Amendment embraces the right to select any religious faith or none at all"); see also County of Allegheny v. ACLU Greater Pittsburgh Chapter, 492 U.S. 573, 589-94, 598-602 (1989); Texas Monthly, Inc. v. Bullock, 489 U.S. 1, 17 (1989); Torcaso v. Watkins, 367 U.S. 488, 495 (1961).
In 1992, the Supreme Court held in Lee v. Weisman, that prayer -- even nonsectarian and nonproselytizing prayer -- at public school graduation ceremonies violated the Establishment Clause of the Constitution.
A school -- and by any reasonable interpretation, a teacher at that school -- cannot proselytize. In any way, shape, or form.
The idea is if we had an official religion, such as secularism ...
Secularism: A neutral attitude, especially of the State, local government and public services, in matters relating to religion.
Secularism: The promotion of secular policies like the separation of church and state.
Secularism: A doctrine that rejects religion and religious considerations.
Secularism: Secularism generally refers to an ideology that promotes the secular (as opposed to the religious) particularly within the public sphere.