I fucking
hate conspiracy theories. I spend (or waste) way too much time online arguing with conspiracy theorists and debunking conspiracy theories. Trump is definitely the conspiracy theorist in chief. It's beyond insanity.
But just like conspiracy theories are irrational, kneejerk dismissing all negative stories as conspiracy theories is also irrational. There's a much more reasonable way of handling this. Things always have to be taken on a case-by-case basis.
You mention boy-who-cried-wolf, and NY Post is definitely a shitty and extremely biased outlet, but probably about as biased as modern day CNN. Both have peddled a lot of hyperbole and unjustified shit, and both have also reported on real things. As far as I know, the NY Post never supported absurd conspiracy theories like Pizzagate or QAnon.
NY Post certainly hyped up Hillary's private email server well beyond the point of reason and fairness, but this scenario would exactly be like if every non-right-biased news outlet all decided to never publish any story even mentioning that she had a private email server that she may have used for non-personal affairs. Of course it'd be extremely irresponsible to have headlines about her email server every day, but it's just as irresponsible to consider the mere existence of the topic an unspeakable matter, as it would be if Twitter were to have censored every link to an article mentioning that she had a private email server she's alleged to have used for non-personal things. This is the Streisand effect in action, here.
It's simply not rational to assume that any story Trump supports is probably untrue. He lies an unbelievable amount, but if you assume 60% of everything that ever comes out of his mouth is a lie, that 40% could still have some real things worth trying to look at objectively. And in this case, this isn't some thing he just peddled entirely himself out of the blue; a newspaper reported on it, even if they're a very biased newspaper. He's going to support anything that he thinks helps his campaign, and not everything that helps his campaign is necessarily bullshit, even if a lot is.
This absolutist stance is part of the thing that only bolsters his constant accusations of fake news - "fake news" has in some sense become a self-fulfilling prophecy in some cases, like here. The left never followed Hillary's proclamation of "when they go low, we go high". Every year, the opposition sinks lower and lower, gradually trending towards the level of the other side. And that's probably exactly what Trump wants and has been trying to trigger.