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First Amendment does indeed prohibit Congress/Government from obstructing the exercise of individual freedoms. As you probably know, it also guarantees the right to believe and practice any religious beliefs, along with the commonly known freedom of speech/expression.
However, despite the specific limitations/prohibitions relative to Government, that amendment along with the Bill of Rights collectively is broader than what you suggest. Civil rights are not conveyed exclusively as a protection against government. You do realize that civil rights actions are brought against non-governmental entities all the time, right?
You also must realize that other protections provided by the constitution (like religion, political affiliation, the right to non-discrimination, etc.) don't suddenly evaporate in the private sector. I may not be a constitutional scholar, but it certainly doesn't appear you are either.