The only real threat here to the Constitution was when a person who's salary was being paid for with taxpayer's money was attempting to stop these men, would probably were taxpayers themselves, from praying.
The 'establishment clause' doesn't mean that people are not allowed to pray in public places, just that the government can't encourage or allow one particular religious group to pray in public while denying that same privileged to people of other faiths.
Read exactly what the 1st Amendment says:
"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."
OCU
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