Getting some models to display correctly in Blender 2.8+

[Sir Teatei Moonlight]

Edit: Hold on, there's a small problem; a few seams have popped up.

Seams like this happen because it's doing some blending with the pixels that are supposed to be outside the range of the face. I don't know if 2.8 has a better way to handle this but you can deal with it in two ways:

1. Tweak the UVs until it's far enough away from the differently-coloured block that the blending is no longer visible.
   
2. Disable texture blending.
   

You probably shouldn't be doing #1 on models you plan to submit; let the user decide whether that's how they want to fix it.