Suppose a government does something to annoy a company, what would stop the company from protesting the action by stopping the sales/providing their services?
For example a hardware company such as Intel or AMD could stop CPU production completely or say that their sales are only for non-government use only.
For a software company such as Google, they could disable their free search and maps services.
Note that those free services have some way for the company to make money. This can be by way of advertising or gathering data which they can sell or otherwise use to make money (for example provide some other service which does make money).
Having said that, a company boycotting a country would generally result in fewer users which in turn leads to less revenue. Even if a company (its management) wants to boycott a country, their shareholders may disagree because they want to keep maximising profit. Those shareholders could oust the management and replace them with those who do what the shareholders want.
Obviously, this answer relies on the company making profit (possibly in the future) based on its services in that country. If the company (or its shareholders) think they cannot make money in that country (not now, nor in future) they are very likely to suspend services in that country.
Doing something like that on a large scale would not be in the interest of the company except in specific circumstances. The company will want to maximize profits and/or shareholder value, so taking themselves off the market unilaterally is just giving their competitors a huge advantage. For example, a removal of Coke from the market will just mean more people will drink Pepsi. If competition isn't a problem, then they are instead a monopoly with a product that can't be easily substituted and has highly inelastic demand. This means that their actions of "protest" just proved that they should be regulated/nationalized from the perspective of that government. An example here would be something like Lockheed Martin refusing to associate with the US government anymore (to the extent legally possible given current contracts, NDAs, security clearances and whatnot), and stating that they will in the future start working for Russia or China. I highly doubt that that US government will be pleased with such a move and just leave things as is.
A timeline of regulation -> "protest" -> repeal of regulation is also highly unlikely not just because of disincentives against "protest" on the side of the company. A government's legitimacy is at least partially based on its power, caving in a negotiation against a company will highly damage its legitimacy. This is a huge disincentive on the part of the government against doing what the company wants. If the balance of power is closer (a very large company and small local governments for example), there is no need for the company to protest since the governments would actively appeal to the company instead, like with Amazon's 2nd headquarter. On a national level with extremely powerful industries, we would see instance of regulatory capture; individuals involved in policy would be from or return to the industries those policies effect. For example, I highly doubt Halliburton would have found any government policy they particularly wanted to protested throughout most of the 2000s. In any case, the level of conflict required for a company to pull their product wouldn't happen, and any problems they have with the government will be addressed in other less drastic ways.
Despite all this there are rare circumstances where "protest" is logical on the part of the company, though the incentive is probably not going to be something like expecting the government to respond positively and repeal the regulation. An example here would be Google in China. In 2010, Google was not performing well in the Chinese market and due to the regulations required to enter the Chinese market a lot of its intellectual property was stolen. It "protested" by removing state mandated censorship on its searches (the great firewall is largely maintained by self censorship on the part of service providers), and this resulted in Google getting booted out and being restricted to operating only in Hong Kong. However, the "protest" was only incidental in this case; it serves as a public relations stunt for those outside China, but Google knew they could no longer access the market and had no expectation of the PRC changing its policy. Google had already decided to exit the market because the theft of intellectual property was hurting it more than its poor performance in the Chinese market was worth. It had learned that the government wanted to cultivate domestic companies, was antagonistic towards foreign companies, and had no expectations of a change in policy. An exit from the market was the logical move, the "protest" was just their attempt to salvage some benefit from the situation.
Some US based newspaper groups (and some other websites) have blocked access to their websites to EU-based users. This is in reaction to the data protection requirements of the General Data Protection Regulation (GDPR), the successor to European Data Protection Directive.
The GDPR requires, amongst many other things, that users can reject the tracking cookies that web adverts use. The GDPR is binding to EU-based companies providing services to anywhere on Earth, but is also binding on companies anywhere on Earth that provide services to users in the EU.
Most large news companies outside the EU now prompt EU-based users for their cookie preferences. However, some have decided that this is too complex, or would affect their advertising revenue too much, and thus have blocked EU-based users.
The Tronc group (Chicago Tribune and Los Angeles Times) is probably the most prominent company, but Lee Enterprises have also made this decision (source).
Nothing would stop them other than the desire to not lose business. Some companies aren't willing to take that kind of loss, but some have principles they hold more important than revenue.
For a fairly recent example, consider encrypted email providers Lavabit and Silent Mail. Both companies chose to permanently close their doors in protest of the US government's domestic spying programs that leverage service providers to turn over user data. VPN provider Cryptostorm has drafted a Privacy Seppuku Pledge stating that signatories pledge to similarly shut down in protest instead of being complicit in what they feel are unethical spying behaviors.
Harassing a company until they leave the market is often a primary goal of the harassing behavior. It works on the same logic as protectionist tariffs. When a dominant company outcompetes your favored competitors, you put a finger on the scale until the competitors are able to compete. Refusing to do business in that market would simply allow the harasser to immediately achieve this goal.
In addition, Google has several times attempted just what you suggest, pulling out of China in 2010 and denying access to Google News in Spain in 2014. Despite harming users in those locations, these protest actions did not accomplish the goal of making the governments back down.
The only force capable of fighting back against government harassment is another government or international free-trade organization, since these organizations have the power of law behind them.
Privately-owned businesses could definitely shut down or refuse to serve a customer as a form of protest, except in cases where that might violate some sort of anti-discrimination law. The problem for "big tech" companies is that these are almost all publicly-owned. The executives are not the (only) owners. In fact, the executives have a fiduciary duty to manage the company in the best interests of its owners -- in most cases defined narrowly as maximizing shareholder profits. If these executives were to deliberately pull a stunt that costs the shareholders money, simply to express their own political preferences, they could certainly be fired, could probably be sued, and in some jurisdictions may even be prosecuted. IMHO that's the biggest obstacle to a big public company carrying out a "political" action.
That said, there are certainly cases of big, public companies engaging in political action and even protests. I seem to recall Apple threatening to cancel a new facility in the state of Arizona if a certain controversial law were passed. At any rate, for the executives to keep their jobs, any political tactics would have to be justifiable in terms of benefits to PR, or marketing/pandering to a particular customer segment, or a negotiating tactic to get more favorable terms in the future or in other markets.
The answer will depend a lot of the locale (laws) and, above all, what sectors are affectd by the boycott.
Discriminating between government and non-government entities could easily go against local trade laws. And of course, even if it is legal, often it will be easily circumvented by using private strawmen.
A second issue is that such a boycott could be illegal if the service/good is needed for essential/strategic services, which are way more protected. For example maybe Oracle could stop supporting the databases used for pet registration, but would not be allowed to stop supporting the databases used for emergency centers/police/public hospitals. And in case the law does not directly address it, emergency legislation would probably be issued1.
And then there is the possible issue of breach of contract, as any sane IT organization will try to protect its operation by ensuring that its suppliers are bound by a contract to ensure that the service is provided in the conditions needed.
1And before anyone asks "Why doesn't the government just protect the pet registration system the same way?", there are usually Supreme Courts and Parliament that can review (even if at a later date) the emergency legislation and object to the abuse of the formula.
Legal obligations
If there is no legal requirement for a company to do business in country X, then there is nothing to prevent said company to end its activities. If the company determines the benefit outweights the lost business, it is free to shut down.
However, if a global company is opposed to the laws passed by a specific country it is unlikely to shut down completely. It is more likely that the company will find a work-around, e.g. facebook moving its non-EU users from Ireland to the US to prevent the application of the GDPR to non-EU facebook users.
However, a company could also restrict its services for a while, e.g. as in the Wikipedia Blackout.
For companies like Google it would be difficult to shut down their "main" services in certain countries. They suppress all competition because they have a virtual unassailable lead (mainly: technology and knowledge about the users).
Should they abandon certain areas they would offer a reserved zone for other companies to learn, grow, improve and earn money. Perhaps one day their competitors would get strengthened so much that they will become a real danger in their main market.
Bottom line: They do not want a "beginners save zone" for their competitors.
I don't know if it's the scenario you have in mind, but in cases where the company is actually supplying essential infrastructure to the government, there may well be contracts in place that prevent the company pulling out. I'm aware of contracts where an IT company has a contractual commitment to support (rather old!) software products for 20 years into the future.
The contracts don't help, of course, if the company goes bust, but in that scenario there are probably escrow provisions that allow the government to take over control and appoint another supplier.
Depending on exactly what the government did to annoy the company, the company could of course try to argue that the government's actions nullify the contract.
As for refusing to sell to the government while continuing to sell to other customers, the law is complex and varies from one country to another. Generally you are free to choose whom you do business with, unless your reasons fall under anti-trust or anti-discrimination rules.
You ask "what would stop the company from protesting the action by stopping the sales/providing their services?"
On the real example in Germany, where they tried to force Google News to pay for the newspaper headline snippets, it resulted in a "Deal". Eventually the newspapers agreed that Google News can show the newspaper title snippets gratis (without paying for).
Some sources say that the loss of clicks was that significant for the newspaper , that they loose more money without Google News.
Therefore actually everything is legal and Google News can show the results.
Just for the record: Google acclaims to not gain revenue from Google News. At least in my country there is absolutely no advertising on the News result page.
