There's the whole, "One man's terrorist is another man's freedom fighter." and "Who decides what is 'extremist'?" points to be made, but pretty clear our society needs to do something to combat the situation. We wouldn't tolerate a drone flying around spray painting hate messages in real life. Society needs some means to condemn.
While there are countries that have instituted massively pervasive censorship, not all countries have, which goes against your argument that governments are certain to do this if given the chance.
I've worked checking images via Amazon's Mechanical Turk here in the US. Pay is low, but you are not required to be mobile and can work at any time.
There are some AI Filters already out there. Probably going to need a regular stream of training data though. I don't feel they'll be able to handle evolving context on their own anytime soon.
You can also simply slightly alter content before uploading. I've even seen people coming out with original uploads after having a neural net process the original material.