This is the First Amendment to the U.S. Constitution:
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 Establishment Clause of the First Amendment deals with the first sixteen words. Congress is prohibited from making laws respecting the establishment of religion or the "free exercise" thereof. This is the core of America's separation of church and state doctrine. While the wording of the Amendment specifies Congress, Supreme Court decisions have, over the years, included Executive Branch agencies of government in the prohibition, since Congress controls the funding of those agencies. Additionally, the 14th Amendment (equal protection) and related court decisions have applied this prohibition to the States. Essentially, no branch of government is supposed to be involved in establishing, favoring or promoting any particular religion. Such activities would be a violation of the Establishment Clause.
The Investigative Project on Terrorism (IPT) has reported extensively about the ongoing case of the Tarek ibn Ziyad Academy (TIZA), a Minnesota public charter school that is run by the Muslim American Society (MAS) and appears to function as an Islamic sectarian school. Those reports may be viewed here, here, here and here. This is one current example of Islam being allowed to encroach into the public domain at taxpayer expense.