It's not a first amendment issue because the first amendment only forbids the government from censoring speech, and private companies are not the government.
However, it's still a free speech issue, and it's still a censorship issue. Just not a first amendment issue.
Private companies can still censor and can stifle/forbid free speech.
No, people disagree on the meaning, scope, nature, and purpose of “free speech”, despite agreeing that “free speech” is a good thing.
It's true that the First Amendment (especially when combined with incorporation under the 14th) directly embodies a reasonably close approximation of one of the viewpoints of what free speech is all about, while simultaneously looking like a narrow special case of one of the other viewpoints.
But the nature of the disagreement here is not confusion between a principle and a legal embodiment of that principle, but a fundamental clash of beliefs about the nature of the named principle.