As a general rule, the First Amendment only restrains the government. It means the government can't ban speech (except in narrow, "content-neutral" ways) and courts can't punish you for it (except for things like defamation).
But the US follows at-will employment, under the more general principle of freedom of association. An employer does't have the same duty to treat its employees "fairly" that the government has to its citizens. Your employer can fire you for pretty much any reason, including differences of opinion, and the First Amendment has nothing to do with that.
The exceptions to this rule are better thought of as exceptions to at-will employment, rather than extensions of First Amendment protection. For instance, you can't fire an employee for discussing wages or working conditions with their co-workers, in the same way that you can't fire someone for being the wrong religion or for reporting illegal behavior.
(If you're saying that the courts should change their interpretation of the First Amendment to include a right to discuss politics at work... well, that would be a major break with precedent, and a huge reach beyond what the text of the amendment says, with wide-ranging ramifications. Instead, some states have passed specific laws that protect workers from discrimination on the basis of political opinion, without needing to invoke the First Amendment.)
That's not what the First Amendment is about - it's about preventing the government from making laws that infringe free speech. But this isn't a law, and GitLab isn't the government, so the First Amendment does not apply.
> It is a common misconception that the First Amendment prohibits anyone from limiting free speech, including private, non-governmental entities. It is applicable only to state actors. (Wikipedia)
That same logic would suggest that no company should be able to ban any topics, content, speech, or people from their platform, no? What is free speech and expression, and what is censorship?
I think society and corporations are wrestling with these concepts right now, and I'm not sure anyone has it right yet.