As others have said, freedom of speech is not the first Amendment and America is not the world. But even American thinkers
themselves define it more broadly, (and always have) e.g.
> What is the liberty of the press? Who can give it any definition which would leave not the utmost latitude for evasion? I hold it to be impracticable... [0]
> Protection against the tyranny of government isn't enough; there needs to be protection also against the tyranny of prevailing opinion and feeling [1]
> Liberty of circulating is as essential to liberty as liberty of publishing; indeed, without the circulation, the publication would be of little value. [2]
Then of course even if what you have in mind is the First Amendment, its whole historical trajectory is to expand to apply to more things. As written it applied to only Congress as distinct from any other form of government, and I note the conspicuous absence of that limitation in how you describe the freedom. And this may be news to some, but we started applying it to private actors long before I was born (Wickersham v. City of Columbia, Brentwood Acad. v. TN Sec. School Ath. Assn, etc.) So it has a long history of ever-expanding scope, and of course when you look at what e.g. Madison thought it was broad from its very birth.
Now we get to
> Well, the real world will never let you have that type of "free speech". If it bothers people... they can start another website/college that allows it. ... In other words, the non-government "free speech" has a cost and sometimes, society doesn't want to pay for it
I'm trying not to poison the well, but this same argument made here has implications for e.g. civil rights. "If you want a hotel that lets black people stay there you can start another one. Racial integration has a cost and society doesn't want to pay for it." But we decided as a society (over many folks' objections) that racial equality was important, and so we wrote legislation. Some people really disliked that at the time; some people still dislike it. However as we no longer have segregated bathrooms I think it is hard to argue that "the real world will never let you" establish human rights, it is actually the story of our country.
You are certainly free to believe that there we have no fundamental human right to expressing a political position on the Internet without living in fear of being fired from our job; that we have come quite far enough, thanks. You can also believe that one's "right" to do that is trumped by other people's rights to contract freely.
But I think in that case one should just admit that they don't see free speech as a fundamental human right. There is no shame in that position. And there is no need to hide behind an economic argument from a dark time in our history, there is no need to accuse folks who do see free speech as fundamental as "diluting" the term or that we live somewhere other than "the real world". Just saying "I don't believe it's a right" is a much faster, tighter, and more difficult argument to attack.
[0] Federalist 84
[1] JS Mill, On Liberty
[2] SCOTUS, Lovell v. City of Griffin