Right, explaining stable orbits will definitely work.

In any case, I think it would make everyone on Earth feel a lot less special if they can look to a place they can never go and see a mirror of themselves... I certainly would expect some manner of incorporation into religion, perhaps as an Eden if the development of religion followed a similar course. A place separate from ours that must be better and therefore the source of all our goods and ills.

Thinking about what it would be like to be the first tourists to the other side...

We're talking about people who think a helicopter being able to hover over a stationary point is proof the Earth is flat because if it weren't, the ground would move away from the helicopter. I'm guessing none of them have ever actually piloted a helicopter before.

I have only piloted a helicopter in a simulator, and every time I tried to hover, the ground definitely moved away and then it tipped over and went splat.

The more “advanced” flat earth explanations account for (and actually depend on) general relativity. I don’t think they’d have any trouble accounting for weather on the moon.