Why doesn't the strong force or nuclear force act entirely differently on protons and neutrons?

But that (tiny 99/100) difference is just caused due to the E/M force acts differently on a neutron and a proton, not due to the strong force. Also note that a neutron is/decays into a proton and a neutron, having slightly more mass.

Also: the strong force acts 'between' pairs neutrons and protons, so it is not as if they are lying in some nuclear-force field which could act differently 'on' them.

The nuclear forces between other possible pairs are indeed different. This is since most of the nuclear force binds the nuclear partical itself together (quarks, and gluons) a residual rest of the strong force is used to bind the different nuclei together. The amount of 'residual' rest that is available for binding nuclei depends on the 'color charge' of the different nuclei.

But forces between other pairs are possible:

proton-proton: the (attractive) nuclear force between them is smaller than the e/m force. not stable.

neutron-neutron: there is a tiny (actractive) nuclear force. but dineutrons are still not bound and extremely short lived. they just recently are measuring the binding energy of it.

noudio apparently lost part of his answer.

The strong force is roughly 137 times stronger than the electromagnetic force at nuclear distances.

So the repulsion between protons diminishes the net attraction by less than 1%. Since the strong force is an extremely short range force (while e/m has infinite [1/r²] range) at larger distances e/m dominates. If you look at the trend in isotope half-lives you will see that stable nuclei require an excess in neutrons. So, p-p repulsion does indeed factor into nuclear physics.

-=-=

I haven't the inclination to look up the cross-sections for neutrons compared to protons of the nuclei, but that, as well as the decay products should confirm the problem with proton rich nuclei. Go for it.