The one bit about the Moon Landing Denial folks I can accept is that they can't believe people were audacious enough to do it 'on a shoestring' like that.
I happen to be a slobbering fanboy of the manned space program, so let me be clear about that. But I can sort of understand if someone now looks at it and says, "that is CRAZY. There is no way in HELL anyone was insane enough to do that." Fair enough, it IS a preposterous, terrifying, insanely dangerous thing.
They navigated using a sextant, clocks and stopwatches. They fired rocket engines manually, and were hand steering a spacecraft trying to lock into a 3-D orbit at an exact second (OK, actually that's 4-D, but anyway, all by hand).
What they are overlooking is these guys were all thrill-seeking test pilots. They did dangerous shit FOR FUN. Today they'd be jumping out of helicopters to snowboard down insane mountains in British Columbia. Back then they flew experimental rocket planes, chased women and drank whiskey. And the twenty or forty BEST of those lunatics put aside all the craziness and got serious because we promised them a ride atop a rocket into Outer Space.
That kind of person doesn't care if he has to use a slide-rule calculator and a sextant to fly to the moon.
I can understand that today it might be hard to believe. The cool part is those old bastards WERE that bad ass. Neil Armstrong's bravest achievement wasn't the moon landing. Read about the near disaster of Gemini 8 and what he did to fly out of trouble. That's the kind of guys who went to the moon. Unbelievable ? Sure.

Awesome, too.