The first amendment also limits companies.
In the US, no company has natural rights. A company exists purely due to corporations law. Any rights a company has, exist only because corporation law provided those rights. The corporations law is subservient to the first amendment. The law cannot therefore allow a corporation to impact upon a human's first amendment right to free speech.
A company could be given free speech rights but that would only apply to speech that is inherently that of the company. It would not apply to employees or customers of that companies as their rights are inherent to the indiviual.
Biting the hand that feeds IT
