You they used to say in the 80's, being robbed at gunpoint will turn any liberal into a conservative. It even happened to Dan Rather once. People thought it was funny for some reason. But being falsely accused of crime, or just being put in jeopardy in our criminal justice system in any way, will turn a conservative into a liberal. But not really. Miranda rights? The rights to legal counsel? The right to plead the fifth? Are those so liberal? The Bill of Rights dates back to 1791. And the English Bill of Rights, which it is based on and derives its name from, even before that. Why are a "rights" a partisan issue in this country at all?
The rights themselves, most of them anyway, don't lend themselves to partisan differences. However, how they are enforced and protected does. Everyone believes is a large measure of individual liberty, but there are striking differences in beliefs about the role of government. One one side, the basic belief is that rights are exercised in the absence of government involvement. On the other side, the belief is that the heavy hand of government must be deeply involved. These opposing views cannot be reconciled, so everyone ends up unhappy. The former group sees a nanny state where the latter group sees the wild west, yet they are looking at the same situation under the same enumerated rights. Their perspectives are irreconcilable. I think that is your answer - disagreement not about the rights themselves, but about the role of government. A short list of subjects such as the death penalty, abortion, and gun control are the exceptions - people really do disagree about the rights themselves, but it's a very short list.