If the person understands why the freedom of speech is important, you can explain that privacy is needed to protect whistleblowers, journalists and activists. Only when everyone has pivacy, it becomes hard for the government to target them.
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.”
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.
Cheapest privacy lesson they'll ever get.
(The point: privacy about who is allowed to acquire the valuables. The owner is in control, not someone else. Once they decide to give that away: fine, now it's no longer under their control.)
Sometimes I think the issue is not being personalized enough, as in, because they do not know the person doing it, it is not an issue. It is an issue if it is you, standing next to them, but it is not an issue if you would be out of sight. It is silly.