I was a Republican. I was always pro choice. I was always skeptical of cops. I thought the Soviet Union and then the rump empire under Putin was dangerous. I never felt "oppressed" by standards of decency. Maybe it's not about being a Republican.
I think the point of the parent of your post and the article is that regardless of what you believe, you should have the right to your opinion and should not be persecuted for it.
If you're referring to abortion, I think the main disagreement between sensible people is the point at which a group of cells becomes a child, deserving of protection? And whose responsibility is that child? My answers are at conception, and whoever is currently in custody (the mother, before birth); simply because I don't see an alternative that isn't highly arbitrary or subjective.
In regard to voting rights, democracy is clearly better than the other things we've tried. I just don't think the people we elect should have quite so much power. Their remit should be limited to the administration of peace and order, not binding us all into one cooperative working towards a common goal. Society is about peaceful coexistence, not collectivizing the realities of misfortune or inadequacy.
Most basically, I think anyone who is drawn to the idea of forcing people to cooperate is taking a moral stance that I simply cannot follow. In the absence of an oracle to divine good from evil, I can't come up with a justification, save one, for using force to compel cooperation. Doing so is indistinguishable from a degree of slavery.