So I discussed this in another question, but Google and Twitter and any other social media site is currently in a legal grey area with respect to Free Speech Laws. As most of these are U.S. Laws, I'll be moving to the U.S. Freedom of Speech laws, established by the First Amendment and SCOTUS Case Law (If I may interject some opinion, some of the most fun decisions SCOTUS will make are about the First Amendment). The United States Bill of Rights (aka Amendments 1-10, inclusive) are best read as restrictions placed on the Federal Government (and the States under the 14th Amendment) that restrict them from performing certain actions against the common people. The First Amendment covers five important rights: Freedom of Speech, Freedom of Religion, Freedom of Association, Freedom of Assembly, and Freedom of the Press (Or more boiled down and in order, the right to say what you want, the right to believe what you want, the right to have relationships with others that you want, the right to access public property for whatever purposes you want, and the right to publish what you want.).
The United States Free Speech Laws are some of the most liberal in the world, but as pointed out, these are restrictions on the government. While you have the right to interact with any group you want and for any reason (activism, fan clubs, businesses, churches, social gatherings, ect) those associations also have the right of association and may make rules to limit their membership (must support our political goals, must like pony cartoons, must want to sell our products for money, must want to practice our faith, must want to Fight for your Right to Paaaarty!, ect).
So Google and Twitter are associations of people who want to make the products they make and sell those services for Money. And Google and Twitter make terms of service for the use of their product and what counts as acceptable and unacceptable content on their platforms. But, Google and Twitter are quite new in just what they do and it's raised the question of what service does Google and Twitter provide: A public medium of communication, or a unique publishing service and this is a distinction with a gulf of difference and to understand the current questions of censorship in Google and Twitter: Are they like phone companies or newspapers?
They're Phone Companies!
The market services of these companies is that they allow you to connect to others in different ways (google by searching for topics you are interested in, Twitter by allowing you to contact others) just like how the phones are used to connect two or more people who will discuss a topic. In the United States, Phone Companies are a Utility Service and are required to allow access to their infrastructure to anyone interested, provided fees are paid.
Naturally, the Phone Company would be nervous about blow back if their phones were used to discuss unsavory ideas... such as a criminal attack, or some racists planning a rally, or winning tickets in a radio-call in contest for the upcoming Justin Beiber Concert. If they are found to be the networks used to provide these communications, they could be sued or punished in some way. Seeing as how it would be bad if phones selected who could access the network based on their customer's opinions, imagine if they Beiber hating phone company won't give a fan a contract and now there is no way to for her to call 911?
So, in order to meet the requirements that anyone who can meet the application process can be accepted, the United States Government will tell phones so long as the bar of entry isn't arbitrary, it will not be held liable for the types of speech that are impermissible that cross it's service. So if criminals coordinate using a phone network, the phone network can't be held at legal fault.
Most vital services are classified as Utilities (Water, Power, Phones, ISPs, Cable, Satellite, and other TV Services... They provide products to everyone equally, so long as they are paying and cannot shut off these products to customers they don't agree with simply because they disagree.
They're Newspapers Publishers
Newspapers (and any publisher really) are similar to Utilities accept that they can edit their products to their liking. This doesn't include just bad grammar, but also which content providers they want to support. After all, if I named a cable news service, you can tell me what type of articles they're going to put up about a particular political candidate. This level of creative decision making allows for content to be regulated and they have a degree of what content makers they work with and which ones they dont. However, unlike Utilities, they are susceptible to lawsuits, such as copyright infringements and defamation suits. They could also be held responsible for content that might encourage illegal behaviors or even some illegal actions they themselves perform in content generation.
Probably the best answer at this time, as the behavior of these companies tends to very to what suits them in the heat of the moment. The people who speak for these companies will claim they merely offer a service when the owner of a picture claims copyright and that they are a publisher when someone sues them for kicking them off for speech they don't like.
As the United States government was designed to be slow and inefficient in passing laws and rules, and social media is a relatively new phenomena, it's still not certain where the matter of Free Speech and social media providers stands at time of writing.
Oh, yeah, the California Connection
Remember how I earlier said that Google and Twitter are both U.S. Companies and subject to their rules... well... the free speech issue gets a little hazier. Not only are these companies all in the U.S. but the vast majority of big tech companies are in California, specifically Silicone Valley. This adds a complication as the California Constitution allows for what is called a "Public Private Space"... this is a little more permissive than the United States right to Assembly, which allows for Public Places only. "Public Private Spaces" is defined as space that is privately owned but is generally open to the public. The prototypical example is a Mall: The entire mall building is privately owned but there are no barriers to entry to the general public during the day to the main common areas between the mall shops. Under California Law, free speech and protest is allowed in these spaces in addition to Public spaces as well. There exists a legal argument that all the above arguments a moot because these companies advertise themselves as public areas for speech (Twitter especially advocates as a public forum). Proponants of this legal oddity argue that while the digital spaces are privately built and owned, the fact that the companies are headquartered in Californian and their infrastructure is there and the fact that they advertise as forums of discussion, many big tech companies are like the space in a mall that are not individual shops... and thus subject to respecting U.S. Free Speech Laws. Again, this is untested in the courts, as the cases that upheld the mall's restrictions on Speech Policing where about physical spaces, not digital spaces housed in California.
- While Generally Free Speech does not apply to private entities, what certain private entities are allowed to do with respect to Free Speech Laws depends on the nature of their services.
- There's no concrete decision as to whether Twitter and Google are more like Utilities or Publishers and they want to enjoy the benefits of being both.
- This all may be moot as they are California HQed Companies and California does extend Free Speech Protections to privately owned entities that act like publicly owned spaces.