My recollection about Wiley Post turning his head from side to side may be faulty, but I recall reading that a long time ago. There may be another factor in his case: virtually all planes in those days were taildraggers. The ones he flew also had big radial engines, meaning that visibility during landing was pretty bad to non-existant. If I recall correctly, most pilots back then had to keep looking from side to side to get a idea of what was in front of them. It might've had nothing to do with depth perception.

As for the Apollo astronauts, I recall reading that all of the landings took place during a lunar morning so the shadows would be longer, giving them a better sense of distance. Still, the landing altitude radar was a critical item. When it began acting up during the Apollo 14 landing, Alan Sheppard hinted that he was fully prepared to go ahead and attempt to land anyway. Odds are, the results wouldn't have been good.