Protons and neutrons, like all hadrons, are color-neutral objects. But, remember that hadrons are made of several color-charged quarks, so the color-charged quarks of one proton can "glue" themselves to the color-charged quarks of another proton, even though the protons themselves are color neutral. This is called the residual strong interaction, and it is strong enough to overcome the electromagnetic repulsion between protons.

THIS IS WHAT BINDS THE NUCLEUS!