That specific series of AMD adapters has a hardware or driver bug that makes the default capture method for game capture fail to function properly with OpenGL games.
Have you tried using the "Multi-adapter compatibility" option in multiplatform's game capture? It will work with OpenGL games just fine, although sadly it'll have reduced performance. This whole situation is almost certainly due to drivers/hardware specific to this hardware in conjunction with the default capture technique.
As the main dev of the program, let me explain why it's most likely not the program's fault. Before I begin, I realize that I sound like I'm defending the program here because I wrote it, but I've investigated this, and I always tend to assume my fault first before investigating just out of caution. So let me go in to the explanation of why you're not getting this with many other programs or when you use the "multi-adapter compatibility" option.
There are two "game capture" techniques through hooks:
1.) Download the backbuffer from VRAM to RAM, the most commonly used technique, the same technique which is used if you use "Multi-GPU compatibility" mode checkbox in multiplatform game capture. This is not as efficient for a program like OBS that also composites, but you'll notice it'll work without issue.
2.) Shared texture capture (essentially shared memory on VRAM that OBS can access without having to download/reupload), which is the very efficent method that can only be used if OBS is running on the same video card as the game. This technique causes the least amount of performance impact to the system, and is the preferred method that OBS defaults to due to that fact. Note that this is always working with Direct3D games because the microsoft windows compositor makes heavy use of this feature, so if it wasn't working with D3D, AMD would have noticed it immediately. However it's far, far more rare to see this feature used with OpenGL, which we do. It's basically an OpenGL <-> D3D interop feature we have to use to get this to work, and you could probably count the number of programs in existence that use this technique with the fingers of one hand.
Typically, most capture programs tend to use #1 because they're not video mixers, most of them just capture and rarely do anything else, so #2 isn't really necessary for them, which is why you don't see it in those programs. In OBS' case, it's an audio/video mixer/compositor on top of being a capture program, and for compositor programs that also capture, #2 is by far the most efficient method to use, but #2 is less reliable due to the fact that it can't work if the game and OBS are on separate adapters.
The first piece of evidence that this wasn't on my end is that I checked the OpenGL capture code, and couldn't find any real flaw in the actual capture code.
The second piece of evidence is that this doesn't happen with OpenGL games on other adapters when using the shared texture method, everything functions as expected. Even older generations of AMD work. It appears to be a driver or hardware issue specific to that generation of AMD hardware when using shared textures and OpenGL <-> D3D interop.
So to sum it up, AMD most likely did not check these specific OpenGL features with their QA, and they possibly ended up storing textures in a specific way internally that causes this graphical distortion issue with OpenGL games using the shared texture D3D/OpenGL interop capture method. Again, it wouldn't happen with D3D because they would have noticed it immediately in the windows compositor. And again, because so few programs on earth use this technique with OpenGL, it's not unlikely that an issue with it would slip past their QA.
That's my best theory at the moment at least, based upon that limited (but important) evidence.
So as easy as it would be to say it's the program's fault, that statement would be unintentionally fallacious if you don't know what's going on behind the scenes. It's very unlikely the program's fault in this case.
Unfortunately you may just have to use the multi-adapter compatibility option until AMD fixes it somehow, if that's possible for them to do.