Yes, calling for a company to fire someone is generally protected under the First Amendment. (There might be some edge cases, like if a state has a criminal anti-discrimination law and someone is inciting the company (to unlawfully fire a specific person specifically on the basis on a legally protected characteristic).)

But the ideal of freedom of expression is broader than limitations on the powers of government. The ideal also encompasses social norms that encourage open and honest discussion. Bad arguments made in appropriate public forums should be met with counterarguments, and certainly not with being placed on industry blacklists or getting fired. Otherwise, there are very real chilling effects on the willingness of people to engage in honest discussion. (To clarify what I mean by "appropriate public forum" above, let me give an example: Protesting someone's funeral by marching on a public sidewalk and waving signs inscribed "God hates X" is legally protected (Snyder v. Phelps, 562 U.S. 443 (2011)), but is outside the bounds of what most people would consider appropriate. Protesting in that place and manner rightfully subjects the protester to public scorn.)