I can let it slide because I don't care. Who cares if someone thinks the world is flat? It's petty and trivial, let people think what they want. If you want to feel better about yourself because you're right, feel that way. Do you have to discontinue a great friendship over it? I don't think so.
In the grand scheme it's one thing. A thing that doesn't even matter. Let's say the world is flat, now what? Nothing, nothing changes, and that's what I'm trying to get at. It doesn't matter.
That's fine. I personally could not. I could not be friends with somebody that disregards reality. Somebody that will believe any conspiracy they hear, because if they believe this then it's likely they believe others as well, like denying people are dead like children, and it's cruel.
If they so willingly disregard they reality around them, where does it stop? They have to have it validated. They can't just keep it in their minds when practically everybody else on the planet thinks they are wrong. The human mind doesn't work that way, it needs assurances that others agree. In order to believe a conspiracy like that you have to believe that pretty much everybody you meet is either a liar or a fool. There is a lot of paranoia, hate, and fear that drives a person to come to such a conclusion. Are they a danger to themselves? Are the a danger to me?
Now, if I was a childhood friend with such a person and we were still close and I found out about this, then no, I wouldn't cut them out most likely. But I definitely would not continue a moderate friendship or be interested in starting a friendship with such a person.