I did a little more experimentation and it appears to be a problem with Godot 3.1 and earlier where the "High Quality Ggx" and "Texture Array Reflections" don't change the sampling count on environment maps for rougher materials. The end result is that very slightly rough materials look "glittery", like someone applied a noise filter to the environment map and then just applied that to the render. I checked the latest Godot 3.2 beta release and it seems to have the opposite problem: turning off High Quality Ggx and Texture Array Reflections doesn't seem to cause noisy sampled environment maps.
Here's a GIF of what I'm referring to:
This is the rusted metal example material that I show modifying the effect of increasing the roughness. You can see that it's not speckled/noisy due to the surface, but because the environment map itself just appears noisy, instead of blurred. It's something I noticed with Godot a year or two ago and appears to be 'fixed' (except that now I don't think you can get back this low-sample-count behavior if you turn down the render quality settings for a project) and might just be something we have to wait for them to fix before you can release a new version that doesn't also have the issue.
At any rate it's not the end of the world and MM is still plenty great for creating PBR materials with. I really enjoy the simplicity of MM and the fact that it is very clean and simple the way software should be.
Also, just out of curiosity, did you develop this using Godot's GDScript?