The Left is dangerous for a number of reasons with its disregard for truth being high on the list. For the Left it is the 'narrative' that counts, the 'script,' the 'story,' whether true of false, that supports their agenda. An agenda is a list of things to do, and for an activist, Lenin's question, What is to be done? trumps the question, What is the case? Paraphrasing Karl Marx's 11th Thesis on Feuerbach, the point for a leftist is to change the world, not understand it. See here: "Die Philosophen haben die Welt nur verschieden interpretiert, es kömmt drauf an, sie zu verändern." "The philosophers have only variously interpreted the world; the point, however, is to change it." (my trans.)
The leftist's aim is the realization of 'progressive' ideals, and if the truth stands in the way, then so much the worse for it. Inconvenient truths are not confronted and subjected to examination; their messengers are attacked and denounced.
For concrete instances I refer you to Jason Richwine, Can We talk About IQ? Excerpt:
So when Larry Summers, then the president of Harvard University, speculated in 2005 that women might be naturally less gifted in math and science, the intense backlash contributed to his ouster.
Two years later, when famed scientist James Watson noted the low average IQ scores of sub-Saharan Africans, he was forced to resign from his lab, taking his Nobel Prize with him.
When a Harvard law student was discovered in 2010 to have suggested in a private email that the black-white IQ gap might have a genetic component, the dean publicly condemned her amid a campus-wide outcry. Only profuse apologies seem to have saved her career.
When a leftist looks at the world, he does not see it as it is, but as he wants it to be. He sees it through the distorting lenses of his ideals. A central ideal for leftists is equality. And not in any such merely formal sense as equality under the law or equality of opportunity. The leftist aims at material equality: equality of outcome both socially and economically, equality in point of power and pelf. But the leftist goes beyond even this. He thinks that no inequalities are natural, and therefore that any inequalities that manifest themselves must be due to some form of oppression or 'racism.' But because this is demonstrably false, the leftist must demonize the messengers of such politically incorrect messages or even suggestions as that the black-white IQ gap might have a genetic component.
This truth-indifferent and reality-denying attitude of the leftist leaves the conservative dumbfounded. For he stands on the terra firma of a reality logically and ontologically and epistemologically antecedent to anyone's wishes and hopes and dreams. For the conservative, it is self-evident that first we have to get the world right, understand it, before any truly ameliorative praxis can commence. It is not that the conservative lacks ideals; it is rather that he believes, rightly, that they must be grounded in what is possible, where the really possible, in turn, is grounded in what is actual. (See Can What is Impossible for Us to Achieve be an Ideal for Us?) And so the conservative might reply to the activist, parodying Marx, as follows:
You lefties have only variously screwed up the world; the point, however, is to understand it so that you don't screw it up any further.
There is a paradox at the heart of the radically egalitarian position of the leftist. He wants equality, and will do anything to enforce it, including denying the truth (and in consequence reality) and violating the liberties of individuals. But to enforce equality he must possess and retain power vastly unequal to the power of those he would 'equalize.' He must go totalitarian. But then the quest for liberation ends in enslavement. This paradox is explained in Money, Power, and Equality.