I use vpn on New Zealand setting but am denied access to a New Zealand site for not being in New Zealand.

Are you using the free, built-in Firefox VPN, Mozilla VPN, or something else?

I'm using the built-in vpn.

And you are in NZ or not?

Generally the built in protection is to conceal the users' personal IP address, it's not designed to fool geofenced services per se. So if the service has a basic abuse protection that rules out non–residential traffic, they might not necessarily know where you're currently, but see the traffic is not a "mere pedestrian consumer"–grade and are blocking access based on that even for NZ egress, if deemed as e.g. "datacenter"–grade.