Actually you're wrong. In the US, freedom of religion is protect by 3 things. The 1st Amendment, the 14th Amendment and the No Religious Test 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.

[...]no religious test shall ever be required as a qualification to any office or public trust under the United States.

Nowhere in those laws does it mention discrimination.

Now, here's the part where you went wrong. There's actually the 14th Amendment which guarantees freedom from discrimination based on several attributes, including religion.... But here's the catch. It only applies to US born or naturalized citizens. It doesn't apply to potential immigrants or tourists.

All persons born or naturalized in the United States, and subject to the jurisdiction there of, are citizens of the United States and of the State where in they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

The United-States government and border control have the right discriminate when it comes to letting someone enter the United-States. In fact, they already do it quite often in airports and at the Canadian and Mexican borders.