[throwaway2568]

Protons and electrons are both Fermions, which means they can not have identical quantum numbers (have to obey the Pauli exclusion principle as mentioned elsewhere in the thread). In the case of a very dense system, like the sun, this can lead to an effect known as degeneracy pressure (which acts against gravity). Essentially you have filled all the lower quantum numbers and then adding an extra proton/electron to the system requires a certain amount of energy. It's quite handwavy but the degeneracy pressure of electrons is mostly what keeps a white dwarf from contracting, whereas in the case of a neutron star it is the degeneracy pressure of neutrons (plus repulsive strong force and other effects as indicated in the OP). This kind of high level discussion is often covered in first year astronomy courses auditing a MOOC like the following may be of interest (https://www.edx.org/course/astrophysics-the-violent-universe)