Exactly the same rules apply in NZ. A convicted sex offender in New Zealand is not denied having a passport. On Border Patrol TV show only last night, a Kiwi with 2 serious sex offences travelled to Australia and was refused entry. He did of course have a NZ passport despite having served two gaol terms for such offences. In that case, there was a determination by Australian immigration that there was no compelling reason for him to come to Australia. Your statement 'no more questions asked' is incorrect, they questioned him extensively.
https://www.immigration.govt.nz/new-zea ... ew-zealand.
More reading
https://newzealand.embassy.gov.au/wltn/ ... ction.html
Ditto USA, sex offenders are issued passports.
https://www.shouselaw.com/ca/blog/can-a ... -passport/