It's less that the first amendment does not apply to minors and more that the first amendment does not apply to the parents' conduct. The first amendment to the U.S. constitution reads (emphasis added):
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.
Thus the first amendment applies to the conduct of the federal government (and has its reach extended to state governments through Cantwell v. Connecticut, 310 U.S. 296 (1940)Cantwell v. Connecticut, 310 U.S. 296 (1940)). The parents' conduct, while perhaps objectionable morally, does not violate the children's rights under the first amendment, as they are neither the state nor the federal government.
