Ok.They both have mass.
This doesn't seem like a very useful use of language. You could just as well say that you and I have an "intrinsic relationship" because we both have mass. What does that tell us? Nothing of any use. Certainly there is no "intrinsic relationship" of this kind in any actual physics. Knowing that the proton and electron both have mass doesn't tell you anything else about them or about their relationships.That is their intrinsic relationship
Actually, they don't. The mass of the proton comes from the masses of its quarks plus the energy contained in the strong interaction field that binds the quarks together.they both have that as an intrinsic property.
The mass of quarks and electrons comes from their interaction with the Higgs field as a result of electroweak symmetry breaking; in the very early universe, before electroweak symmetry breaking happened, quarks and electrons were massless.
None of this changes what I said above.