What Plans? said:
Even if the starfields were similar, that could easily be explained as stars which are too distant to change position in the sky.
The one background which had always royally pissed me off, even as a kid, is the final scene of ESB when Luke and Leia are looking at the distant galaxy. That galaxy is huge in the sky, but even so, it would still be at LEAST a few MILLION light years away. Which means that it should have been visible in every single starfield in the entire Star Wars saga. There would not be a single place in the galaxy that you could go without seeing it in the sky.
Just like, even if Earth got moved to the other end of the Milky Way, much of the night sky would actually remain the same because of the light coming from stars in galaxies outside of our own.
There seem to be some general misconceptions about how visible other galaxies are to the naked eye (or a film camera). The closest galaxy to ours of any considerable brightness, for example, is Andromeda, which is ~2.5 million light years away. Astronomically, that's very close. Can we see it? Just, with the naked eye. It doesn't and never could appear like the image we see at the end of TESB. The images you see of Andromeda are about 400 billion dots of light which, from a distance, appear to form a whole. The closer you get, the lesser this appears. Galaxies are simply not dense or bright enough to be that visible to the naked eye. So it can't be a galaxy. Not that it really matters if it were intended to be, as it looks nice, and it's irrelevant to the story what it was meant to be.
As for starfields not changing... Well, if you don't move far and you are looking in the same direction, sure, you would see the same arrangement of stars. But if you move to a different system, absolutely the starfield will change, completely. The more distant (and generally less visible) stars might move less to begin with, but all the nearer stars would change relative positions. Identifiable constellations, for example, would be the first to go, and then your sky is truly different. The only time part of a starfield might look the same is if you move further away from a particular point of view but facing the same direction; again, after a while it will all change. No-one else in the galaxy gets to see Orion like we do :-)