Two rights colliding is essentially an unstoppable force meeting an immovable object. The two can not (should not) violate each other, thus one's rights end where another's begins.
Governments are also tasked with guaranteeing those rights, and those who violate another's rights are deprived of their rights as mandated by laws.
For example, a murderer (violator of another's right to life) is imprisoned (deprived of his right to liberty) and possibly even executed (deprived of his right to life).
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.
Governments are also tasked with guaranteeing those rights, and those who violate another's rights are deprived of their rights as mandated by laws.
For example, a murderer (violator of another's right to life) is imprisoned (deprived of his right to liberty) and possibly even executed (deprived of his right to life).