> is it antidemocratic to advocate for a Parliamentary system over a Presidential system?
It depends on the law (constitution). If the law says it's forbidden, then it is anti-that-kind-of-democracy. If there is no such law, then it's consistent with democracy.
Real presidential democracy should allow for change of law and constitution, so the democratic process here would be to first change the law/constitution to allow for advocating, then advocate for switching to Parliamentary system, then get this change passed through the lawmaking process. Lots of steps, very hard to do, but in principle there should be a legal and democratic way. If there isn't legal democratic way, the system is highly suspicious, and probably isn't even formally a democracy.
> If we didn't, should the NZ government be able to ban a party advocating for one?
If the government (in extreme, the president) is democratically elected, and if the ban is done constitutionally and lawfully, then that would be still democratic.
> Germany supports lots of antidemocratic measures. They oppose binding referenda of the population before the adoption of international treaties
Interesting, is this an official government position with some rationale? Or the government just does whatever they can legally and ignores the calls for referendum?
One rationale I've came across is that international treaties (in parliamentary systems) have to go through the parliament, which is representative, so referendum is not needed, and if someone wants to invoke one, they have to do the necessary work required by the law.