Hello!
The specific version of MacOS the textures failed to render in my case is High Sierra 10.13.6
Also this mac has an ATI Radeon HD 5750 graphics card.
I have also tested the application on:
Windows 10.0.19042 Build 19042 with NVIDIA GeForce GTX 650 Ti BOOST graphics card
Itch.io HTML5 version on an IPad (iOS)
These do not show the same problem.
Here is the render on the MacOS specified:

Here is the render on the Windows specified on itch.io:

I have uploaded a HTML5 version to itch.io here if you want to test it:
https://pureimprov.itch.io/spatial-trainer
Things I have tried:
---Changing the Import settings on the textures from vram to lossless - however the textures in the 2D GUI load fine, it
appears that the textures loaded into an albedo on a SpatialMaterial resource are where the problem lies
---Changing the renderer in godot from GLES3 to GLES2
---In Project Settings > Rendering > Vram Compression I have changed from Etc 2 to Etc - I did this before I realised this wasn't a browser/html5 specific issue
https://github.com/godotengine/godot/issues/24465
--- I have tried using different textures
---In a previous version of the game the SpatialMaterial textures loaded fine on the specified MacOS device. Since then I have
changed the SpatialMaterial on ALL 4 3d scene models by setting a MeshInstance's GeometryInstance > Geometry > Material Override to a new SpatialMaterial. This doesn't seem to point to an instancing/directory problem though as one of the SpatialMaterial textures is a direct child in my main scene. I am also unsure whether the Geometry Material Overide is the cause but it could be.

It is a sort of hybrid graphics driver rendering/godot project related because the inconsistencies between devices is tied to how I've set up my project. I can't quite pin this one down, I have considered shader lighting issues i.e. the MacOS setup does not process my Environment's light but this doesn't seem to be the case as it worked fine previously with the same Envrionment.
I am really just curious to know why there is an unusual conflict between this particular machine set up and me changing some SpatialMaterial Textures in my project (or perhaps something else I forgot I changed). Maybe you can replicate the issue on the itch.io HTML5 application on different machines. There are mipmap warnings in the web inspector console (I also tried changing turning off mipmaps) that seem to be related to cube maps but I can't imagine this is related especially as it only applies to the face.
Maybe I will never solve this but hopefully the information will provide useful to someone.
Some other posts that seems to show similar issues:
https://github.com/godotengine/godot/issues/43855
https://github.com/godotengine/godot/issues/24465