Landscape Backdrops?

Why do the hills in the background of many of the photos keep reappearing in other photos, but with different foregrounds?

What can often be seen in the background of the Apollo lunar photographs are not hills, but mountains. Very big mountains, even compared to mountains on Earth.   Lunar mountains tend to be big because there is nothing to wear them down, unlike on Earth.

It is also very difficult to judge distances on the Moon.  This is because there's no atmosphere to soften distant objects and the landscape is pretty featureless. So things that are very far away can appear to be quite close, unless you know their relative size it can be hard to tell.

Take this unassuming little hill pictured here.  Doesn't look much, does it?   In fact this is Mount Hadley, all 4,500 metres (14, 765 feet) of it.   That makes this "hill" over three times the height of the tallest mountain in the British Isles and bigger than any mountain in the US outside of Alaska.  And Mount Hadley is by no means unusual in lunar terms.

So these 'hills' are actually mountains, and they're far away. So the astronauts would have to travel a long distance before they'd ever stop being in the background.

What Apollo photos taken from different points actually show is a slight variation in the angle you can see the mountains.  This is called parallax and is often used on Earth to estimate distances from photographs.  Parallax is very hard to fake and would be impossible with a 'backdrop'.  Rather than proving they're a fake background, the photographs prove they are three dimensional, large, distant objects.