Not 100% clear on the question to answer it, but I think I know what your getting at. As a rule of thumb, if something is true you have a responsibility to believe it. The problem is not necessarily what someones believes- it's what actions those beliefs lead to.
For example, some people have argued that Jesus Christ did not exist- it would undermine Christianity, perhaps fatally and will affect how they behave around Chistians. Will they be hostile for instance to Christianity or to religion in general? If someone says that Jesus was White, does that affect how we percieve white people as having a civilising mission on behalf of Christiainity? If someone says that the Confederacy fought for states rights, it ignores or diminishes the role of slavery and white supremacy in the US civil war. Or that the US was founded as a Christian nation, in relation to how a person reads the First Amendment seperation of Church and State.
If someone denies the Holocaust took place (or it's Soviet eqivilent, the Ukranian Terror-Famine or Holomodor), it dramatically changes how a person evalutes Nazism (and Communism) and -thought admittedly unlikely- increases the chance that they will play a role in perpetuating any future atrocities. If someone denies climate change, they may continue to support putting greenhouse gases into the atmosphere.
On a less political area, think of what happens if someone doesn't accept the law of gravity, or a ships navigator doesn't believe the earth is round, or that a magnetised compass points to the magnetic north pole.
In so far as knowledge is common property, it is a general "loss" to mankind if we selectively ignore our ancestors experiences and the lessons we can learn from them. what we ignore, what we deliberately try to forget can have much bigger influence on how we see ourselves, what actions we can justify and the consequences we have.
Ignorance has consequences as does our Knowledge. In particular, propaganadists know this and can exploit our ignorance to unwittingly serve their cause and this is why "historical revisionism" and "Anti-Science" are such a powerful weapon in their ideological arsenal. By attacking the truth they can affect people's perception of "reality" and therefore their behaviour. By being informed, we can improve the chances that our consequences will be good.