Ah, the old slippery slope argument. Whether or not Twitter has a responsibility to fact check tweets, they absolutely have a right to do so.
Its too bad the author didn't give some examples to back up this boldly stated opinion
Personally I would say that whether a tweet deserves a warning is mostly independent on whether it is factually true. It is far too easy to lie with only factually correct statements.
The partisan condemnation of her reporting, and the BBC's craven response, have been widely ridiculed.
Facebook applies dubious “false info” fact-check label to Patriot Act video https://news.ycombinator.com/item?id=23356373
Your right not to be forced to publish someone else's words is a more important application of the first amendment than someone else's right to force you to publish their words.
If you're a major figure in international politics intentionally spouting actual lies, then your lies should be exposed.
If you're encouraging violence your posts on a private medium then that private company has every right to remove that content from their privately owned platform.
This post said that they randomly "decided" to start enforcing the policies. They've been enforcing them on everyone, just not Trump because he has demonstrated time and again that he will threaten and penalize any company or organization that doesn't act as a completely subordinate organization to him personally.
Twitter has clearly had enough and decided to make him aware that he isn't a special and unique snowflake. He doesn't get any special treatment. He doesn't get to encourage violence. He doesn't get to outright lie to the public.
If he doesn't like those rules he can go off to 4chan, or dailystormer, or wherever else he feels sufficiently safe and coddled.
No one is censoring him for his skin color, his religion, his beliefs, his political view point.
He isn't being censored for being POTUS, or Republican, or anything else.
His false statements are being linked to "here are the actual facts" documents. Those posts are still completely visible, there is no censoring, he just not being given carte blanche permission to provide objectively false information.
His threats of violence, and encouragement to that end are the only things being hidden by default - you can still see them.
The latter is still not equivalent to your argument. Not even remotely.
I don't get to reject to serve someone because of their religion, gender, orientation, or race. But if someone comes to my store and starts shouting that we should harm other people, then yeah I do get to kick them out. There is no debate here.
Racists and the like always love to compare suppression of threats and calls to harm others to denying service to others on the basis of who they are.
Twitter doesn't kick nazis or homophobes off the platform. Unless they start calling for harms to others or actively state that other people don't have the right to exist.