implications != truth value

This is a symptom of people who either do not think critically or people who hold off on thinking critically about certain aspects of their lives.
You know the people I am talking about- people who refuse to believe something or even consider it because of "what it would mean".
This is such a strong cultural phenomenon that it has become a common plot point and aspect of stereotypical characters.

The problem with this argument is that no matter what the consequences of something being true are, they do not make it any less true.
For a bad example, holocaust deniers are not always white supremacists- sometimes they are people who are simply nieve. People who don't want to believe the horrible things that happened because that would simply mean that horrible things have happened in the past- unimaginably horrible things.
For a more realistic example, most western Christians deny a lot of things to themselves, but one strikes me as particularly offensive. That Atheists have morals that are equal to or even better than their own, and that they follow them. That can't be, because that would mean they either aren't morally superior, or that they don't have a monopoly on morality, or that morals are a conclusion you can come to on your own, without God's intercession.
This idea is so frightening that it is more often than not shut completely out of their thoughts, dismissed as an impossibility.
Another disturbing example is one of creationism- people taking the oversimplification of it too far and then being offended that they may share a common ancestry with many modern primates today or "that my grandma was a monkey".
Or that we are not "any different than the animals"(of course, larger brains and better adaptability, as well as culture and language makes us completely the same as animals.) and thusly not "special".
This kind of thinking is infantile at best, and destructive at worst.
The scary part is that they are allowed to teach this to their children.