IMHO, the problem isn't just fake news but a broader, and longer term problem of general dishonesty in society that's been going on for decades.
* Government dishonesty since at least Viet Nam and/or Nixon. Two examples where the government actively lied and/or stretched the truth, and there are many others. This has long been internalized by many people about the honesty of government.
* General misleading nature of advertisements. We're constantly bombarded with misleading messages about every day items and we've all had experience where the product doesn't align with its promises.
* Corporate dishonesty -- outright lying. Karen Silkwood, Thalidomide, Corvair, Pinto, corporations relentlessly covering up and lying about bad products, corporate misdeeds and so forth. And these are all very old examples just to demonstrate how it has been going on for decades.
* Employer dishonesty -- The relentless messaging from management about business goals and plans for employees. How often is it true or does it end up improving employee work lives? Almost never. Most people impulsively parse and disbelieve what management tells them because it's so often the opposite of what they're told.
* The near-legal practical status of scams and cons -- We're constantly assaulted by outright dishonest people. Spam email, "card services", "free cruises". Yes, it's illegal and few people believe it at face value but there's so little effort to stop it that it seems to be legitimized as a means of doing business.
* Ideological dishonesty -- across the political spectrum all ideological advocates both embrace untruths necessary to advance their cause and discount their critics when it seems patently obvious they're not being honest.
It's not just fake news -- belief in fake news is just a symptom of the relentless, never ending crisis of honesty in our culture. Lying and misleading is so ingrained in our culture that doubting is our first impulse. So why not buy into fake news and conspiracy? Lies and conspiracies have quite often been shown to be true, why should I have any faith that person/institution X is telling the truth and not lying to me and that the conspiracy is false?
Until the Internet, the news media was actually one of the last institutions to *mostly* tell the truth -- libel laws, the business nature of actually printing news, journalism as an actual profession with a sense of ethics and some mission to tell the truth -- mostly worked against fake news, which was (in the US anyway) generally marginalized into corners of celebrity gossip or supermarket tabloids. It just wasn't practical to create fake news when you needed a press run of a million copies on a regular basis and a distribution network.