Some religious discrimination in the US is legal, but it depends on by whom it is being committed, and it what context. The first and 14th amendments prohibit discrimination based on religion (or, in the 14th amendment's case, in general) for the federal and state governments.
The First Amendment:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech
The Fourteenth Amendment:
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.
Since Bolling v. Sharpe, a Supreme Court decision from 1954, the Fifth amendment has also been interpreted to imply equal protection under federal law. The fourtheenth amendment applies only to the states.
Religious discrimination by the government is subject to the standard of strict scrutiny, which means that the discrimination must be necessary to further a significant government interest, narrowly tailored to further that interest, and must be the least restrictive means of doing so. Otherwise, it's unconstitutional.
Private discrimination against religion is also regulated: the Civil Rights Act prohibits religious discrimination in hiring, payment, employment benefits, etc.
However, hate speech in the US, including hate speech targeted at religion, is legal in the US. The First Amendment guarantees freedom of speech, and the Supreme Court ruled in R.A.V v. City of St. Paul that the fact that laws against calls to violence were constitutional did not mean that laws against hate speech were constitutional, as hate speech did not constitute "fighting words".