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I think these info are correct, even some banking apps got unlock via fingerprint option for Latest Galaxy phones, but never saw it for Xperia. Let me escalate this and try to find a proper answer.
Ok, what you were told is not correct, it appeared that Sony's fingerprint scanner is directly connected to the Fingerprint API developed by Google so it's up to the app developers to support this.
So if it's not working with an app then the app developer needs to extend support to Xperia Z5 family. What I suggest is to try more apps, and contact developer of those apps that won't work.
The guys on XDA developers say that Marshmallow will allow generic app support, and thus your only choice if you can't find a suitable app at the moment is to wait till Android 6 lands.
Latest known application to work with fingerprint access to open it is 1Password, but it needs Marshmallow.
Hope Sony will send us the updates quickly, it's so frustrating !