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No it isn't, if a reasonable excuse exists.
That’s the point. The default is that it’s illegal to open other people’s mail.
Nope, not after delivery. Have a look at the Postal Services Act 2000. S84(1) says you can't open post while it's in transit without good reason, but S84(3) is clear that once it's delivered, it's only an offence to open it if i) you intend to cause detriment to someone, AND ii) you don't have a reasonable excuse.
No intent to cause detriment, no offence.
Reasonable excuse, no offence.
No it isn't, if a reasonable excuse exists.