A certain someone was out tonight doing some exploration, and got to thinking about the moon as it's currently out and bright as fuck.
Got to thinking about how manuals often say "Don't position yourself between the moon and your target."
This is true to an extent, but it can also be wrong. Generally, you don't want to be between the moon and people in a very literal sense. If the moon is behind you, it's going to silhouette you and cast big shadows. However, if the moon is higher in the sky, it can actually give you the advantage while behind you. Consider the fact how difficult it is to see into a dark area when there's a light above. It's fucking hard, because your eyes focus on the light too much, causing a sort of haze over the dark area. Same applies with the moon. If you stand in a big open area, notice how easily you can see things with your back to the moon. Now face the moon. You'll probably have to form a visor with your hand and still not even see quite as well.
So, when the moon is low, don't get between it and a person. If the moon is high, position yourself there so that it can make you harder to see and give you the visibility advantage. Similarly, be especially careful about people who could be between you and the moon, as they can see better than you.
When the moon is high, be careful going down hills facing away from the moon. The moon will project a shadow reaching all the way down the slope, and silhouette you all the way down. If you need to be extremely stealthy, this is one of those times to low crawl.
Finally, no matter where the moon is, always keep a low profile on high areas. Never stand on hill tops, crest, edges of buildings, or anything else that's going to form a black hole. Remember, vision in the dark is based on contrast, not color.

Since I'm writing so much, a few tricks:

When the moon or any other light is giving you a hassle seeing past it, form a box with your hands (think of making mock binoculars, but as one hole rather than two). The box will stop light from coming into your lateral vision and allow you to focus on dark areas.

Always travel below the crest of hills so that you don't silhouette yourself. Standard technique.

Keep the fact that night vision relies on contrast rather than color in your head at all times. Shape to a certain extent. With the moon high and behind you, you can almost always see people before they can see you, and that's including if the person is actively searching for you. If what you CAN'T see bothers you, move yourself into the appropriate position to get the superior vision.

In urban areas, the moon generally won't do you a damn bit of good. On rooftops though, it can hurt you. When the moon is bright, never stand on a roof. In fact, always make sure your body is pressed against something when you are near ANY edge. If you're beside a building, be right next to it. Don't stand on the side. Again, contrast. Everyone knows the building will be it's own dark spot. If there's a dark spot next to it, that's irregular. Standing next to it let's the building "absorb" your silhouette, so you become just another part of it.