for clarification, they are being continuously separated

This is an exercise in restraint. You must be able to criticize your opponent as you would criticize yourself: constructively, with respect, and without mercy.

I would suspect that the main differences would be almost entirely neurological, because physical differences are a result of moving successfully through a native environment, and those would be roughly the same. I think republicans would evolve into a colony like ants, where a small number are turned into “ruling class” hominids through specialized transcription factors in breastmilk. These individuals would have relatively higher intelligence, at the expense of the parts of the brain that allow for strong emotions or empathy. The rest of the colony would be practically identical, with heightened senses of fear, anger, and religiosity-derived joy. They would have a strong sense of cohesion, but anyone that does not fit into the society would be quickly killed in violent mobs. There would also be higher levels of sexual dimorphism, with men and women being hyper-genderized to the point that it causes health problems.

Progressives would become hyper-individualistic, and hyper-aware of social pariah rules established by their society. They would dissolve the idea of gender, and sexual dimorphism would even out and you wouldn’t be able to tell someone’s sex by looking at them. They would be matriarchal but have weak social bonds, because of the individualism. They would also reproduce much more slowly, with the average age of first childbirth happening in middle age.