There are hundreds of good arguments for a right to privacy. This isn't one of them.
There is a real temptation for people to think "Society is generally fine the way it is, so I don't want things to change", which makes them react negatively to things like protests or even whistleblowing (because it causes them cognitive dissonance).
Such people might feel confident that even if the government did abuse its power, it would only spy on, or silence, or hurt people who aren't like them. They therefore may not feel that these fundamental rights are doing them much good, and they don't consciously exercise them. However, many of them would exercise their right to vote, and could imagine the government turning against them if there were no more elections.
You can also try Edward Snowden's analogy:
“Arguing that you don't care about the right to privacy because you have nothing to hide is no different than saying you don't care about free speech because you have nothing to say.”
Sadly I worry that many people don't care about freedom of speech either. I wonder if such people would also be unmoved by this analogy:
“Arguing that you don't care about the right to privacy because you have nothing to hide is no different than saying you don't care about the right to vote because the party you support is currently in power.”