Ultimately it's a very hard problem to solve.
Fake news, and its far more dangerous big brother, propaganda, can have an enormous effect on a society. Providing people with tools to identify real information from fake information seems like a great thing for those who want to use them.
But a lot of folks (whether they realize it or not) want to see fake news because it confirms their personal worldview (or: how everyone loves confirmation bias) and makes them feel good about being part of their in-group.
I suspect folks who push for censorship think that it will somehow ensure these types of folks don't consume fake news or propaganda (probably without realizing that they, too, have consumed fake news from time to time).
But the reality is fake news has existed for a very very long time. Hell, you could tune into MSNBC or Fox News and find stories that border pretty closely on fake news without even trying. And, again, they do it because it increases ratings. And it increases ratings because it makes people in their respective demographics feel good.
So what you're ultimately trying to fight is the human need for a sense of belonging, and the desire to feel good about their personal beliefs. Good luck with that...