To reproduce:
1. Open attached project
2. In the assets, navigate to Materials > UI > Mari_DIFF and delete the material
3. Reimport the texture located at Textures > UI > Mari_DIFF. A material is created and Material.mainTexture = texture is called, but the texture does not get assigned. You can inspect the newly created material at Materials > UI > Mari_DIFF

The script has no problem setting the material color, but it just can't set the main texture.

This is by design. We do not support assigning references to objects created by the importer.

The PersistentManager doesn't know about the newly created object until after the Import has finished, and as such the reference is lost when the object is unloaded.