O.k I’ve updated my .blend.

Should get rid of this issue:

The 180° rotation of the texture is now no longer depending on the location of the geometry, but uses a Noise Texture turned binary 😉
The use of Pi and e is random, could have used any number, but for randomness, avoiding integers is never a bad idea…
For completeness, this is the link:
https://drive.google.com/file/d/1YIo8HAvCjkyoIU05m9dRpWQrjKZxdB85/view?usp=sharing