According to Crystal Field Theory, d-orbitals of central metal atom splits due to non uniform repulsion of ligands around the metal atom. Why isn't p-orbital splitting discussed?
To be blunt, the reason nobody mentions p-orbital splitting or non-splitting is that neither the teacher nor the learner has ever understood the crystal field theory properly in its true depth (including myself). They just propagate what they saw in standard textbooks, repeat the same in class, the students pass never to see CFT again. The story ends. If that student ever becomes a teacher, the story continues.
You are mixing apples and oranges. Crystal field theory has nothing to do with hybridization. The original work of Hans Bethe, the man behind crystal field theory, wrote a 72-paged highly theoretical paper in Annalen der Physik in German. The translations are available and I quote the abstract where he does clarify what happens to p-orbitals. How many can claim that that they read this paper completely before teaching CFT. I cannot. The abstract clarifies your misconception.
The influence of an electric field of prescribed symmetry (crystalline field) on an atom is treated wave - mechanically . The terms of the atom split up in a way that depends on the symmetry of the field and on the angular momentum I (or J) of the atom . No splitting of s terms occurs , and p terms are not split up in fields of cubic symmetry . For the case in which the individual electrons of the atom can he treated separately ( interaction inside the atom turned off) the elgenfunctions of zeroth approximation are stated for every term in the crystal; from these there follows a concentration of the electron density along the symmetry axes of the crystal which is characteristic of the term. - The magnitude of the term splitting is of the order of some hundreds of cm-1. - For tetragonal symmetry, a quantitative measure of the departure from cubic symmetry can be defined, which determines uniquely the most stable arrangement of electrons In the crystal.