Okay, this requires a lot to unpack, but I'm going to try here. For the purposes of this discussion, I'll use two "controversial" statements one that will be agreeable to most US society including Facebook ("I like Fireworks on the Fourth of July") and one which is not ("Nickleback is the greatest band ever"). These are meant to avoid actually really nasty political issues, but still provide examples of speech that is largely agreeable and largely disagreeable and both are neutral to each other (You can agree with both statements, or disagree with one but agree with another, or agree with neither statement, or have a combination of no opinion on either statement).
The First Amendment and Business and Employers
So the First Amendment (and the Constitution in General) restrict the government, not the citizens. The First Amendment is generally seen as protecting the Freedom of Speech, but it traditionally protects Five Core aspects: Freedom of Speech, Freedom of Religious Worship, Freedom of Association, Freedom of Assembly, Freedom of the Press.
The government is permitted to limit speech only in ways that are content neutral. So if the government says "You can't burn ads for the big FoJ Fireworks show because it is unpatriotic" this would be unfair to the few people who dislike fireworks shows as a form of protest and to noted fan of Nickleback, Wade Wilson, who don't have similar protections for their posters advertising the Nickleback concert. However, if the government makes a law that says "You can't burn ads in protest because there's a bad drought and it might cause a huge wildfire" then it says nothing about the content of the product being advertised, and thus is a reasonable restriction of a form of Protest.
Private people and businesses are not restrained by this restriction and thus a fireworks store does not need to hire someone who hates fireworks and Wade Wilson can't be restricted from forming a Nickleback Fan Club with his good buddy Ryan Reynolds. Even the U.S. Government can restrict employees from certain political speech (hence why the Army, which is a Government Employer can restrict what the grunts say about certain Political matters... the Hatch Act is pretty much a law that bars those employed by the government from certain political activities, where as Facebook can restrict employees from expressing certain ideals it does not enjoy.).
So what service is Facebook?
This is the $64,000 dollar question. At present Facebook wants to be regulated like a utility provider (like a phone company, an internet provider, a power company, ect.) they also want to be able to retain certain content they don't want to associate with (like Anti-Fireworks messages or Pro-Nickleback Messages). These two product entities are mutually exclusive in this regard.
A utility provider cannot engage in view point discrimination because they have too much power over peoples lives. Suppose Pro-Fireworks lovers want the power company to ensure the best shows by cutting all power to the city on the Fourth of July or Anti-Nicklebackers want the company to cut power to the building that houses their Fan Club. These negatively impact people in various ways... Anti-Fireworkers might want to play video games with their buds and Pro-Nicklebackers might lose their rented space in the building, because the other tenants want their power turned on. To say nothing about a hospital patient who needs life saving surgery during the power outage. In order to prevent the unpopular opinions of customers from affecting such vital services, the companies cannot be sued because... let's say Mr. Wilson was trying to convince Mr. Reynolds to kill all Anti-Nicklebackers (Mr. Wilson isn't right in the head, after all)... or because doctors need electricity in the ER at all times. Facebook wants to be classified as a utility as this will immunize it from defamation lawsuits (for example, I, just moments ago said that Mr. Wilson is a crazy person with out evidence to justify my claim... he could be completely sane with 4 out of 5 doctors agreeing... which means I could be sued for slandering his good name (I didn't slander him. I libeled him. Slander is spoken word). However he won't sue me because I make no money, and cannot sue Stack Exchange because they are just a utility service provider that I used to express my opinion).
However, if Stack Exchange takes steps to remove my above libelous statement, then it is not a utility service, but a publishing service (Like News Papers, Movies, Fictional Books), which means that they lose the immunity to libelous suits by third party users... as well as any images a share, real people who I made false statements about (Maybe Mr. Reynolds), Fictional Characters I didn't properly source (Like Mr. Wilson's fictional status as being owned by Marvel Entertainment, which I do not own, and his creator was Rob Leifeld, who I am thankfully not) or used in violation of copyright (Fair Use, suck it Deadpool!). Facebook similarly does not want to be a Publishing Service, not because it wants to provide service for all, but because being classified as a publishing service means it's now opened up a floodgate of lawsuits onto itself... sure, it could fight most, but the sheer amount of stuff on Facebook that is actionable is damaging enough that it cannot fight every... some will hit it and they will hit hard.
So in effect, they kinda haven't been classified as either for what protections and rights they can claim, so they take the best of both worlds... which only invites regulatory authorities to look at the rule book and wonder if they can regulate social media as a third unique class of services.
Is Facebook a Monopoly (which is illegal in the United States)?
No. Since we're talking about unpopular opinions, you can always use MySpace, right? Of course, Facebook isn't the only Social Media service in town... It's just the one all the cool kids you want to interact with use at this moment. It's not stopping you from creating your own social media site... with Blackjack... and Hookers (Fair use, Bender!). And it's not the most popular social media application the world over. Russians love Livejournal (dunno why) and the Japanese love Twitter (mostly because 148 characters in Japanese is a good five paragraph essay in English, in terms of information it conveys).
However, just because Facebook has commentators, doesn't mean it's not a Trust... basically, Facebook and several other social media web sites have in the recent past engaged in cooperative behaviors to simultaneously ban popular political commentators from their services within hours of each other, effectively locking out these individuals from any major alternative social media services. Basically, the accusation is that while not a monopoly, the bulk of the market share of social media worked together in a coordinated anti-competitive effort, which is the legal definition of a Trust in economics, which was such a big work around to the "No Monopolies" act, that it was made illegal in the same exact law... and actually named in the law's title (The Sherman Anti-Trust act) and the action of breaking up monopolies is called Trust-Busting.
The other alternative is to just not get involved in Social Media. These people do exist in the United States... it's not all encompassing and because social media can be addictive, it's probably advisable if you don't need it... That said, there has been recent discussion that Facebook has started "Shadow Accounts" for non-users. If you never use Facebook but your best friend does, and he posts about how you two enjoyed a restaurant or a movie, Facebook will create a file about the non-user and append the data to the file... if you in the future sign up and friend your best friend... Facebook will try and find the Shadow Account of best fit and append that to you. This is all to market advertisements for you, which is how they make the money (if a company provides you a service for free, you're not the customer, you're the product. McDonald's sells burgers. But if you get all your food, and care, and comfort for free from McDonald's, you're not the customer, you're the cow). And yeah, it can be scary in that regard (though for me, Facebook has gotten some critical details about myself hilariously (and offensively) wrong.).
Back To Free Speech
The reason this all matters is because the Road to Hell is paved with good intentions. Sometimes, popular and well like ideas do have downsides that are valid. Anti-Firework people could point out that they're Veterans with PTSD and the noise of the Fireworks will trigger that condition. They aren't unpatriotic, they made painful sacrifices defending the very ideas those Fireworks represent (or more neutrally, avoiding the Fireworks at Disney Theme parks because they know that all the popular rides are empty of riders during the display). And Nickleback fans might not be tone death mental basket cases... they could just be from the same country Nickleback comes from and want to support their fellow country men (Or they like a select few songs, but don't care for the rest... like they do with every other band they encounter and they think Nickleback is unduly maligned.).
There's a famous magic trick by Penn and Teller where they burn the United States Flag, not in protest of the nation it represents (as the act often symbolizes), but in moving tribute of said nation. George Carlin's famous "7 Dirty Words You Can't Say on TV" mocks censorship by being so bold as to name the seven words out loud and then pointing out that the ration of words you can use vs. the ones you can't is 399,993 to 7. He would later deconstruct the list by making fun of the pronunciations of the words, their appropriateness on the list 30 years after the initial bit was told, and the fact that the sixth word was only wrong because it also included the fourth word but he refused to remove it because the list was now so iconic, it would break the flow of the list and make it too short. There's only one use of any of the seven words in a non-meta context in the entire bit.