No. It means that there will be no established, official, Federally sanctioned religion. No Church of America, as was the case in England with the C of E.
The Religious Wars were not far in the past for the Founders, and they didn't want that sort of thing starting here. In 1776, the Spanish Inquisition was still around. It wasn't abolished until Napoleon took over Spain.
So many misunderstand the language and parsing used in the days of the U.S. Constitution's creation, and as used in the 1st and 2nd Amendments. So sad.
Some people read the 1st to mean that congress can't make a law that respects religious establishments; they can only be disrespectful. It's unbelievable. And scary. Thank you, public schools.
"An establishment of religion" is an establishment of what ever you decide the word "religion" means.
The word "religion" was used during the founding era to convey many different ideas may very well have included a church,synagogue, established official Federally sanctioned religion or the C of E.
However, in the context of a fundamental legal safeguard for the "rights of conscience" the word "religion" often meant "the duty we owe to the Creator." Some examples are the "freedom of conscience" amendments to the U. S. Constitution recommended by the Virginia and North Carolina Ratification Conventions.
My rules of strict interpretation require me to search for the meaning of "religion" first in the text of the amendment, second in the understanding of the men who ratified it and third in the legislative history of its framing. The Virginia and North Carolina recommendations are found in the legislative history and I judge then to provided the best definition of the word.
In 1878, the Supreme Court apparently believed that there was no other possible meaning for the word "religion" in the First Amendment other than "the duty we owe to the Creator. I believe that was a reasonable view warranted by legal and moral principles.
Wherefore:
CONGRESS SHALL MAKE NO LAW RESPECTING AN ESTABLISHMENT OF THE DUTY WE OWE TO GOD, OR PROHIBITING THE FREE EXERCISE OF THE DUTY WE OWE THE CREATOR.