It's a comedy show. The fact that people accept it as fake news is cognitive dissonance to negate the truths that are often exposed by the satire. Many fans generally "get it" that it's the funniest thing because it's true. Critics and detractors dismiss it as "fake news", or 'liberals bashing Republicans for entertainment', so they can also watch, laugh, and not learn a damned thing. It isn't fake news. The news and events being lampooned are usually real. It's the reactions or the angles that are lots of times played completely straight, but still end sup being ridiculous. Comedy news satire, but they need it to be "fake".
And then you see "Conservative" comedy which is an entirely different kind of beast altogether.