And in muslim countries, if someone posts LGBT or atheist positive posts, they should immediately be moderated and the poster reported to authorities.
Facebook should also prevent users from these countries seeing such content posted from more liberal places.
This argument, if applied strictly, would allow any government to meddle in the affairs (say, influencing elections) of any other government simply by establishing ostensibly private companies that'd perform to their wishes, whether overtly or secretly. That being anti-democratic, there's clear need for limiting actions of private companies.
While I am against compelling speech, I do not consider Facebook a newspaper publishing its own editorial content, but rather a platform for publishing third-party content. In fact, posts on Facebook are clearly attributed to the author, which, with minor exceptions, is not Facebook itself. On the other hand, official communications of Facebook are marked as such and clearly delineated from users' posts. Thus preventing Facebook from deleting posts (i.e., forcing them to let posts remain) would amount to preventing them from performing (the seemingly arbitrary and capricious) censorship, rater than compelling them to speak.
For me the line is clear - illegal content must be removed, legal content must be left undisturbed, and if Facebook considers law of some country to run counter to their conscience, do not operate in that market.
The only problem is, since the internet is free and open, whether Facebook operates as a legal entity in a particular country or not, doesn't prevent internet users from that country to access the services. And Facebook doesn't have any obligations to ban IP ranges from that country. So, it's the country's responsibility to ban traffic to Facebook.
Facebook should not accept instructions from Hungarian government. Now it's "Please don't remove videos from our minister", tomorrow it will be "Please immediately delete any bad comments about our government. Oh, and that opposition candidate's page? Delete that too"
Facebook's community standards should not be universally accepted. Does anyone force Hungarian people to use Facebook and accept their community standards? No. But if they freely choose to use it, of course they are expected to accept the rules of the community they willingly chose to participate in.
I am not a Hungarian, and I don't care what the Hungarian government is doing within their own country. If they want they can censor newspapers, ban TV shows on local media, close the borders, not have foreigners in their country, whatever. But they shouldn't influence foreign media the same way that they cannot ban a TV show airing on some Croatian television because Hungarians near the border can catch it...
Shit, the US isn't a democracy? I don't think this is how any of this works.
They shouldn't rely on this as their only option, but they may as well ask. If the publisher complies it saves everyone a lot of bother.