People just want their own sense of superiority validated, which means that people tend to believe what they want to believe. This is the sentiment that the Boys from Lagos exploited for example: the belief that the recipient has somehow been specially chosen to perform this special job and get rich from it, and a lot of people still fall for it today, despite it being relatively common knowledge.

The playing field is nowhere near as level as you believe it is. Truth is almost always a middle ground, and the middle ground just doesn't interest people. The more outrageous the claim, the more interest it gathers, whereas the more mediocre the truth, the more likely it is to be ignored.
People are very rarely in favour of actual freedom of information - when most political interests quote "freedom of speech" and "freedom of opinion", what they actually mean is that they want to level the playing field to make it easier for them to gain control of the flow of information.

As you say, far-left anarchists claim to be all in favour of absolute freedom, but frequently stoop to censorship and strict moderation on online forums. Far-right extremists claim to value freedom of opinion, but really only want to have a soapbox to shout out their vile views with impunity, again to gain control.

I guess we just have to disagree with that. For instance, all the people I personally know are neither neo-nazis nor anarchists, and have no sympathy for either. Most people at least here seem to want to stay in the middle ground.

Also, I feel common people do quite often feel angry if someone had fed them false information, even if it was something they'd otherwise agree with.

No it is not.

Internet is a medium, not the goal.
you can use it well, you can use it badly.
Online there is everything, both serious sites, both sites to avoid.
What we must do is not to say that the internet is shit, is to teach our children to use it.
Many parents were born in an era pre-computer, they find it difficult to learn, so they leave their children without a guide.
It's like leaving a knife, can be used for cooking or to kill someone, if you do not know how to use it you can cut yourself.
If the parents instead of using the computer / tablet / smartphone only to facebook / twitter, learn to use these mediums they may teach their children how to use the "knife" in the right way.
Blame the internet is like blaming the knife because it cuts.
The same can be said for censorship, if the parents were aware their children there would be no need for censorship.

Sorry to say this but things went to shit long before the internet was invented, probably somewhere when mankind decided to become 'civilized', the internet just accellerates the general state of things.

A good carpenter doesn't blame his tools.

Because dear Brutus, the faut does lie in the stars but in ourselves.

You mean a truth like "the internet is okayish, has benefits as well as some issues" is more likely to be ignored than an outrageous claim like "the internet is shit and society has definitely worsened because of it"? ;)