[somerandomqaguy]

Yes they can conflict. I chose slavery because it did conflict. 13 States left succeeded from the United States to form the Confederacy to protect slavery at the behest of their own citizens. And the remaining Union disagreed. Violently. The US Civil War was one of the bloodiest in it's history.

Even today. SCOTUS overturning Roe vs Wade and allowing States to prohibit abortions. A difference because of a disagreement on whether or not a human embryo is entitled to be treated as a full human being with all the same rights and responsibilities.

Hence the nuance. You can look at the same document that says these rights, but how they are achieved and what limits there are can differ due to differences in opinion.