Well... that's not quite correct. Private companies cannot do whatever they like.
They cannot engage in discriminatory hiring practices based on skin color, gender, age, or religion. They are not supposed to refuse service. Remember the case of the bakery that wouldn't bake a custom cake for a homosexual wedding? The baker was willing to sell them a standard cake but wouldn't create a custom cake. It went to the supreme court, which decided that custom cakes were a form of art, and you cannot force someone to create art. Youtube, Google and Twitter cannot claim they are creating art.

I really do not know where to start, so I will go bit by bit.

Are you talking about the Colorado case? If so, please have another look at the details.
What SCOTUS decided was that in Colorado, the state had a bias that was unconstitutional against the baker - and this is what tipped SCOTUS in favor of the baker - not, as you claim, that baking a cake was a form of art.
https://www.foxnews.com/us/supreme-court-decides-colorado-gay-wedding-cake-case-a-timeline-of-events
Justice Anthony Kennedy said when the Colorado Civil Rights Commission made its decision "it did not do so with the religious neutrality that the Constitution requires." The opinion says the Commission "violated the Free Exercise Clause, and its order must be set aside."
In its decision, the Supreme Court did not decide whether a business has the right to refuse to serve gay and lesbian people outright.
Political belief is not explicitly protected, but a strong argument can be made that it falls under religion, which is a protected category. Religion and political belief are 'philosophy of life'. This is something that atheists and a-religious people should have no problem supporting
https://law.justia.com/constitution/us/amendment-01/09-freedom-of-belief.html
“If there is any fixed star in our constitutional constellation, it is that no official, high or petty, can prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion or force citizens to confess by word or act their faith therein.”
567 Speaking in the context of religious freedom, the Court said that, although the freedom to act on one’s beliefs could be limited, the freedom to believe what one will “is absolute.”
568
But are Youtube, Facebook, and Twitter even private companies? Most would agree they are PUBLIC FORUMS because of their sheer size and the fact they use the internet, a public infrastructure which they do not own. Twitter CEO Dorsey stated to Congress that Twitter is a public forum. Because they are regarded as public forums, they are exempt from certain types of prosecution. If they claim to not be public forums, then they should not be granted those exemptions, and they should be broken up, or put under government control like the parks and public roads..
This is highly speculative and at this point, not legal precedent.
Phone companies cannot refuse service based on what people say on phones. The postal service cannot refuse service based on what people write in letters. What makes Facebook any different? What gives them the right to riffle through people's private pages, selectively banning things they don't like?
First, phone service and the postal service are almost certainly considered absolutely necessary for modern life. Fakebook and all the other "social media platforms" are not. People can just drop fakebook and use the telephone, or write a letter that they send through the postal service. Slower, yes, but gets the job done.
Second, the postal service cannot open mail. The recipient is the only one that can do that. As well, the phone company cannot legally listen to any conversation on the phone.
However, with the postal service, a recipient can file a form called Postal Service form 1500 "PS-1500" for short, that makes it a felony for anyone to offer something to you for sale that you find objectionable for any reason, and the postal service cannot make that determination for you.
https://en.wikipedia.org/wiki/Prohibitory_Order
Not only that, though, you can take a threatening letter to court, or the FBI, or the postal service itself and seek injunctive relief. The same applies to similarly threatening phone calls.
In addition, people are still free to peaceably assemble, per the 1st amendment, at any place that will lawfully allow them to do so. Even in this day and age, I think it is a difficult point of view to some how support that "social media" is indispensable to modern life.
Also SCOTUS has ruled that 1st amendment rights do not include speech that incites violence. You will have to look that up yourself. Its out there. If any "social platform" leaves speech that incites violence on their site, they may be held legally liable if such violence manifests, or, perhaps, they may be charged with aiding terrorism.
These corporations are like bandits that control a narrow river passage on a public river. The river funnels enormous amounts of business to them because there are no viable alternatives. Yet they deny service to some, claiming there are viable alternatives. They want it both ways.
Social media companies aren't the only villains. Financial institutions like Paypal, Chase, and others have refused service and terminated accounts of conservatives. Universities refuse to allow conservatives to speak on campus, or make it so unsafe and difficult that it's almost impossible
If a university thinks that any speaker may create an environment that is unsafe, I see no problem in them refusing to host the speaker.
You make some great talking points, but, as I see it, the jury is still out on whether or not there is undue bias in any platform.
The first amendment Freedom of Speech clause was created to protect political and unpopular speech. Banning speech because some find it offensive is absolutely no excuse. The principle is that all views must be allowed to be heard in the public forums, where the incorrect ones can be defeated on the merits through proper debate
Once again, 1st amendment rights do not include inciting violence.
But Facebook and other politically motivated institutions want to short-circuit the process and stifle public debate. They don't want the public to even know that there are opposing views, let alone hear them. That fact tells you they do not believe they can win the public debate. It should be cause for serious concern.
Thanks for your opinion, however, like I said, there are other means to organize.
Most multimedia companies have shut down their comment sections. They couldn't handle the overwhelming amount of conservative anger. They trivialize the anger by re-labeling it as 'hate'.
Progressives believe they are infallible.
Thanks for your opinion.
But that was disproved by the recent Mueller Report. Mueller spent three years with a highly partisan team investigating accusations of Russian collusions and obstruction of justice. He determined there was none. If there were, he would have indicted Trump. The progressive arguments were defeated on the merits.
With Trump binding and gagging everyone in the matter at this point, it is difficult to separate belief from truth. When the gag no longer applies, and at some point that will happen - particularly when Mueller's employment at the justice department ends in a month or so, we might see what the truth really is.