Does an atom or proton (cosmic ray) get stretched when traveling through expanding space?

Neutrinos are fermions, and physicists believe that neutrinos from the Big Bang have redshifted to lower energies as the universe has expanded. This has not been experimentally verified, because neutrinos are fiendishly difficult to detect.

You should not think of this neutrino redshift, or photon redshift either, as the particle stretching. The stretching is a wave effect. The particle is just losing energy. It remains a point particle, if we neglect the effect of quantum fluctuations. A point particle cannot get larger and still be a point particle!

As for atoms, there is similarly no experimental evidence. I would think that they redshift but that the orbitals do not stretch, because the orbitals are determined by electromagnetism, not by gravity.

All waves propagating through the universe get stretched as it expands, and by wave-particle duality all particles, elementary or composite, have wavelike properties. In the case of a hydrogen atom moving through intergalactic space, the relevant wave getting redshifted is the de Broglie wave of the entire atom, not the waves of its constituent proton and electron. Those waves are confined within the atom and are not propagating across the universe.