Majority of our beliefs are vulnerable to "peer review". There is nothing negative about that, because otherwise, we'd all be spending time verifying everything anybody says.
The only thing I am saying is that you should not try to discredit anyone for holding a set of beliefs, because we are all guilty of similarly not vetting the truth. Very rarely do we dive into establishing the facts fully, because it would be impossible to talk about anything.
If you disagree, let's go through an exercise. So your car says it's now going 60km/h. I can't trust you or your car, let's put side markers on the road, and I'll use a stopwatch. We'll also have to do like 100 runs, and change the surface a bit so we control for skid (non-slippery, slippery...). Ok, for those side markers, how do we measure them? What about the time? I'll drop by Paris to get 1-true-meter and compare my stopwatch with their atomic clock to ensure the error is within, say, 1%.
All this is the vetting required for a basic, easily measurable "fact". Anything involving the human mind, it's nigh impossible.
You should discredit the beliefs (if they are not factual), and discredit people who knowingly spread misinformation. AND you you should question at least privately whether they truly hold those beliefs or merely say they do.
Rumors. Think why spreading rumors is considered bad and unethical? It is because many people will believe them and thus get mislead. And whoever spreads the rumors typically somehow gains from doing so, perhaps simply by getting the attention of other people. When you get people to listen to you, and "believe" you, you are in a better position.
However, on the topic of "if they are not factual", how do you practically check that? Seriously, do you exclude all prejudice, and if I give you two contradicting sources, how would you establish which one is "factual"?
> We can just say that the fact is that the speed meter reads 60.
(As an aside, my car needs software recalibration at the dealer if I switch to differently sized wheels: if I don't know to what wheel size software was calibrated to, I would need to verify it)
"Just say" is a manifestation of a "belief". The question is how do you, in a grand scheme of things, establish if it's not a "false belief"? You are, ultimately, putting your trust in somebody else doing the verification (of a speedometer in a car, in this example)!
Basically, it is our hope that actual facts will "surface" through this chain of trust between people into majority of people's heads, but throughout periods in history, that was not the case: eg. think Middle Ages; or any of the propaganda initiatives by the modern media.
As an obvious example of such a modern media play, I am sure you'd find most of the people in the USA before the Iraq invasion believed Iraq had been actively developing WMD. A quick search gives me this (I have no idea how trustworthy the source is, but such caveats should be assumed in human communication):
> Moreover, the share of the American public that believed it was “very likely” that U.S. forces would eventually uncover Iraqi weapons of mass destruction fell from 59 percent in early April to 39 percent in late April.
(From https://www.brookings.edu/articles/rally-round-the-flag-opin...)
As far as we know, at least 59% of Americans had "false beliefs" prior to the invasion, and even after troops were there, 39% still maintained them!
In accepting that it's too easy to have false beliefs promulgate, we open ourselves to an ability to develop tools and processes to combat that. But I truly wonder what are the practical tools we have to do that today? How is a "regular" Jane or Joe going to do that?