Privacy provides a fundemental protection from persecution by your government. This is precisely why the constitution includes specific privacy protections.

So while we should fight governments that persecute homosexuality, we also need to protect at least some aspects of privacy to keep protections for the next persecuted group.

Should we avoid preventing further damage that the domestic company is doing? Or should we limit ourselves to dealing with the issue diplomatically, and not do anything else for fear of "looking at the wrong problem"?

I don't understand why you'd seriously suggest that reducing the likelihood of known harm (by ensuring some level of privacy) is the wrong thing to think about when it doesn't prevent other actions from being taken too. It's possible for groups of people to do different things at the same time, after all.

Ultimately, your argument will never result in a situation where privacy is taken seriously because you could substitute in any issue and your conclusion could just as easily be that "better privacy is looking at the wrong problem."