That's certainly not a universally agreed upon perspective. Just because you're a private company doesn't mean you can do anything you want (eg. discrimination), hence the existence of regulations.
https://www.theguardian.com/technology/2018/jul/02/facebook-...
Whether the company is private or not is immaterial. What matters is its scale, and how much you can actually avoid it.
Facebook is not easily avoided. I personally went under significant social pressure to get an account and actually use it. Getting out had a measurable cost (not being aware of events that mattered to me). That's not too bad, but even then I'm cheating: my SO has an account, and I regularly profit from that.
Same for YouTube: they have a near monopoly on most western audiences. If they block something, that's near censorship. Next to it, most alternatives might as well not exist at all.
Facebook's handling of filtered out messages is honestly not an improvement over WeChat worth celebrating.
Why does this not apply to other situations such as who I hire?
Also, is not Facebook used by parts of the US government? If Facebook prevents me from sending that link to any government representative then does that not constitute the government (by choosing to use Facebook as a communication channel) censoring my speech? It would be similar to the case of Trump blocking individuals on Twitter. Imagine if government offices swapped to some religious based chat forum as their official means of communication where messages from all people not of a certain religion (as determined by the sight) are filtered.