How can diamond have a fixed refractive index?
Your textbook is wrong. Some crystalline solids are optically anisotropic. Many crystalline solids are indeed optically isotropic in nature. In solids like this the light beam experiences the same electron density regardless of the direction the crystal is oriented. Some examples of that are (obviously) diamond, halite and sylvite (sodium and potassium chlorides), garnets, spinels and more. Note that this is a feature derived from the electronic structure and it has nothing to do with the actual shape of the crystal.

Even in the case of anisotropic crystals, some are so weakly anisotropic they may considered isotropic in practice. Zeolites are a perfect example of those.