The Tango messenger app is probably the worst app for privacy I have ever come across. If you have any concern for your privacy at all, you should not use it. Below I will list just a few of the things that concern me as far as privacy and the Tango app.
Tango saves all your contacts to their server
When you install the app on your phone, it seems to try to sync with all the contacts in your phone. Although there is a setting to stop this called "Save Address Book to Tango" under "App Settings", this setting is on by default and by the time you have installed the app and want to turn this off, it is too late and your contacts have already been saved to their servers.
It sometimes allows people to see your phone number
This one really surprised me and it has happened about 3 times to me. I have opened the app and instead of a contacts name being displayed, tango displayed their phone number. These contacts were only tango contacts who I had never met and who had never given me their phone number. I even checked that is was actually the person's phone number by sending them a regular text and surprisingly, it was their actual phone number. This problem seems to me like it has something to do with the person changing their name in the apps character encoding
You can't remove contacts
For some reason, in the Tango app, contacts are added just by chatting to someone, for most people this probably isn't the behaviour that is expected so if you install the app and go about chatting to many people, your contacts will grow quite fast. To add to this, you can't actually remove contacts, you can only block them.
The "Access my Location" setting under the privacy settings only affects future locations
Under the "Privacy settings" of the app, there is a "Access my Location" setting. This setting seems to affect the location that is listed on your profile and also affects your profiles showing up in the "discovery" feature when people search near a curtain location. The problem I have found is that even when turning this setting off, the last location that the app found is still saved, being displayed on your profile and still allowing people to "discover" you in that (last saved) location
These are just a few of the problems I have found and the sad new is that if you are already using the app, your data is already on their server and as far as I know, there is no way of removing it
Also, it seems that the makers of Tango have a new app called Fiesta which is pretty much the same thing. I would advise people not to use that app too as it probably contains the privacy issues that Tango does.