Emulator

Is this the same issue as the following one? https://bugs.dolphin-emu.org/issues/8388

Not quite. The other issue wants to add new color combinations but it wouldn't allow users to manually adjust those colors. That feature request wouldn't help my problem as red-cyan is already implemented but I need to make adjustments to the color for proper display.

Could you upload a screenshot of the game? I mean, not a photo through the glasses
I'm pretty sure it's a problem with your glasses (A glimpse of cyan light through the red lens), since it's a very common issue, but a screenshot would really help. It could also be a screen issue, tho (If it's a tv, it's more likely to be a tv post-processing issue. You should try to disable all post-processing filters the tv could add, since it also creates lag. Most tv's have this option as a Game or Graphics video mode)
Also, you should try the green-magenta combination. It has less noticeable artifacts and is way more comfortable than the red-cyan combination (let's not start talking about biology). The only caveat is that green-magenta anaglyphic is only available on OpenGL (Yes, I'm the one who requested it).

Now that 5.0 has been released I'd like to look into this issue again. I have Visual Studio 2015 but I've only used it to compile a debugfast version of Dolphin. If I could be told the file(s) or code(s) that control the anaglyph shader color I'd be willing to try editing it myself.

Stereoscopy support in the OpenGL backend supports different Anaglyph shaders. When setting the stereoscopy mode to Anaglyph the post-processing shader will switch to an Anaglyph shader.

The default is the dubois shader, but you can select other shaders. You can even write your own shader if you want to completely customize it, you don't need to recompile Dolphin, you can just put the shader into your Documents\Dolphin Emulator\Shaders\Anaglyph folder. You can see an overview of the source code of the default shaders here: https://github.com/dolphin-emu/dolphin/tree/master/Data/Sys/Shaders/Anaglyph

Note that the type of color bleeding you've shown is normal for anaglyph glasses if you want to see a bit of color. If you're fine with not showing any color you can select the grayscale shader which should have less color bleeding.

I didn't realize Dolphin can load custom anaglyph shaders from Documents\Dolphin Emulator\Shaders\Anaglyph. Since that allows me to relatively easily modify the shader this issue can be closed.

I'm still hoping that DirectX (including DX12) gets post-processing shaders but that issue has already been made.