In this particular case the privacy thing is quite easy to get around, don't answer any questions at all, and for when the usage is required (like court cases) either don't ask irrelevant probing questions and in the case of therapy it probably doesn't matter as they have pretty tight privacy things already.

I'm kind of amused by anyone that would use a religious rights argument here as i"m pretty sure most mainstream religions are pretty big on telling the truth XD

I think the real reason people would hate something like this is because they'd be forced to tell the truth to themselves and a lot of people almost exclusively prefer their "comfortable lies" XD