>The First Amendment applies to restrictions to speech from the government, but provides no rights or privileges when it comes to repercussions from private entities.
This is generally true but there are exceptions, which funny enough you acknowledge one of them in your comment.
The National Labor Relations Act (NLRA) gives private-sector employees the right to discuss their working conditions, which is considered “protected concerted activity.” They can share information about pay, benefits, safety and other work-related issues — and they can do it in the break room, at happy hour or on social media (such as Facebook and Twitter).
Real-world example of workplace freedom of speech:
Situation: A group of employees who worked for a retail store in San Francisco were concerned about their safety due to their store’s closing an hour later than other nearby stores. After unsuccessful discussions with the manager and later, the owner, the employees posted their frustrations on Facebook. An employee who saw the posts showed them to the owner, and subsequently, the other three employees were fired.
Ruling: The National Labor Relations Board reviewed the Facebook posts and determined they were acceptable. The employees were discussing the store’s legitimate safety concerns, so the posts were considered protected under the NLRA. It was determined that the employer committed an unfair labor practice by firing the employees.
What is otherwise not protected speech becomes protected speech.
>Correct, but this isn't why they were fired.
Amazon published a press release on the matter acknowledging they fired the employees for their posts about safety in the work place...it doesn't matter Amazon claims the post violated company policy, these employees have legal right to discuss their working conditions, which is considered “protected concerted activity.”
As you may or may not know the NLRA protections come from the Constitutional Right to association, which is an essential part of freedom of speech. While the United States Constitution's First Amendment identifies the rights to assemble and to petition the government, the text of the First Amendment does not make specific mention of a right to association. Nevertheless, the United States Supreme Court held in NAACP v. Alabama (1958) that freedom of association is an essential part of freedom of speech because, in many cases, people can engage in effective speech only when they join with others.