Ok, so first off we need to get a better idea of the sizes and distances involved here, because that image just doesn't cut it at all. Under RE

this image is a to scale representation of Earth and the moon for sizes and distances. This Earth is about 1/8 inches in diameter (actual diameter is about 8,000 miles) and the moon is 3.75 inches away (actual distance is about 240,000 miles away) with a diameter of about 1/32 of an inch (actual diameter of about 2,000 miles). Using this same scale, the sun would have to be over 1 foot in diameter (actual size diameter is about 864,000 miles) and the center would be about 121 feet from the center of our Earth circle. These distances are very hard to comprehend and deal with, and it's why scale images showing all three barely exist.

But, these give us some very useful numbers. With the diameter of the Earth, and the distance to the moon, we've got everything we need to create a triangle! This will give us the angle of the largest difference between two sides of the Earth, which will tell us how much difference each side should actually expect to see in their viewing angle of the moon. Very helpfully you even used an

angle calculator earlier on another thread, so let's see what we get when we plug things into this, shall we? I'll use the same notation as your calculator so you can follow along.

Side lengths (Used M since your calculator doesn't have an option for miles, but using the same numbers means we won't change the angle results)

side a: 8,000 (Diameter of Earth representing the two people on either side of it.)

side b: 240,000 (Distance to the moon for person C)

side c: 240,000 (Distance to the moon for person B)

Plug these in and we get

angle A: 1.90995 °

angle B: 89.045 °

angle C: 89.045 °

So that means, angle of viewing difference between two observers is only about 2° at the outside. I would note even placing the moon at a 90° angle to one of the observers still leaves us with that same angle. What does all this mean?

Firstly, because of the size of the sun, the Umbra and Penumbra cast by the Earth are both quite small. In fact the Earth's Umbra by the time it reaches the moon (due in part to light curving through the atmosphere) doesn't actually block out the moon fully. But even in the images created by intikan, the moon at a full 90° angle to one side of the Earth, the other side will only see a difference of just less than 2° to one side. Which isn't all that discernible to the human eye, especially considering the shifting the moon goes under on it's own. I'd be more than happy to work on delving more into this issue, but this should provide a good foundation.