Some school playgrounds have bars high enough above the ground for kids to hang upsided down from if they wish. If you hang upside down from an outside bar and happen to see the Moon while doing so, you are looking at the moon (while you are) upside down.
That is the only possible way for the phrase "looking at the moon upside down" to make sense.
If you look at the Moon with your eye, the part of the Moon which looks like the upper edge to you will actually have a higher angle above the horizon than the part that looks like the lower edge to you. You will be seeing the Moon upside up.
And possibly someone in the southern hemisphere looking at the Moon will think that your lower edge is higher than your upper edge, and your lower edge will actually be farther above his horizon than your upper edge will be above his horizon. And so he will be seeing the Moon upside up from his position, even though what he sees is upside down from your position.
If you look at the Moon with the naked eye, you will see the Moon in a position which is upside up from your vantage point.
Lense and mirrors invert images. Telescopes use different combinations of lenses and/or mirrors. So if you look at the Moon though a telescope the specific combination of lenses and/or mirrors in the way the telescope is set up at the moment will determine whether the image seen thorughthe telescope is inverted or right side up.
If you are looking at the Moon though a telescope, you can glance at the Moon with your unaided eye to see if the pattern of light and dark areas is the same as though the telescope. If they are reversed, you will know that the arrangement of lens and/or mirrors in the telescope inverts the image.
And if you become familiar with the geography (selenography) of the Moon, you will be able to recognize the north and south polar regions of the Moon. Then when you look at the Moon through a telescope, or look at a photograph of the Moon taken with a telescopic lens, you will know which pole of the Moon looks "up".