This question is inspired by this Washington Post piece ("Donald Trump is working his way through the 1st Amendment").
Here's the amendment text, 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.
The author's first note says "The 1st Amendment curtails Congress, not the president." It goes on to quote Trump talking about shutting down mosques, blocking Muslims from entering the US, abridging the freedom of the press, etc. and there are a lot of things a President can do without Congress.
Could Executive Action be used to prohibit the free exercise of religion, etc., within the broad authorizations of executive authority that the President has (from Congress or otherwise)?