As it is known, editing the registry of Sacrifice is the way to achieve 1920x1080. However, this causes issues with objects popping in out of the world. What I was wondering is, is it possible to set the game at a 4:3 resolution, and stop the game from stretching? I mean like just having black bars at the side, rather than the game taking up the whole screen. I think this would make the game more appealing to look at, UI wise.

It's already been discussed many times. Why didn't you check first?
For example here: https://www.gog.com/forum/sacrifice/flickering_with_gog_version

The best method for getting an actual widescreen resolution seems to be this one (http://www.wsgf.org/dr/sacrifice), involving replacing a few files in the game installation directory.

Halfway down that page is a link for 'Sacrifice.7z'. Extract the contents of that archive into your Sacrifice game folder (it will overwrite some files) and you will be able to select your 1920x1080 resolution from the in-game menu. I hope this response proves more useful to you (and to others).

So you whined about him starting a new thread, and linked to another thread where you whined about someone starting a thread? I bet you're a blast to hang out with.

There's direct solution posted there as well as few links (especially the last one) to the solutions posted before. But you propably didn't even read that and still you're first to accuse me of whinning and being unfriendly (I bet you know me very well). Of course you didn't add anything new to discussion except calling me names. Typical. I wish I had report button somewhere here.
Btw sacrifice forums here are not updated frequently with new threads and IF you've read them you would have seen posts even from april 2013 at the first page. That means it's not too hard to check for previous threads/solutions for frequent problems because most of them are on the first page. That's why i don't like asking same questions over and over. Of course you know better though.

Weirdly enough I seem to not have the bug (tried only 3 games though).

I know that on the Steam version I got I used the registry fix and I had the disappearing objects/enemies.

But now I installed the GOG version, got the widescreen fix from here http://www.wsgf.org/dr/sacrifice and, maybe important, I didn't change any other graphics option, aside from the resolution (I did that in-game with the mod obviously, not through registry).

I'm on Windows 10, and have GTX 560. Playing in 1920x1080.

It seems both the links at www.wsgf.org/dr/sacrifice have been taken down.
Would someone be so kind to reupload it somewhere?

If anyone still needs it, here it is:
https://www.mediafire.com/?udiv1mpatacub5h

A permanent place to download the Widescreen Patch.
http://www.moddb.com/games/sacrifice/downloads/sacrifice-widescreen