The main reason why the Netherlands at least doesn't care so much about their monarch is because the role is completely neutered by the Dutch constitution. The King or Queen functionally has zero power over much of anything - their role is pretty much entirely ceremonial in purpose (they can theoretically choose to not sign laws, but this would just result in them getting sidestepped).
This is in very stark contrast to the UK monarchy, which does hold very considerable power and control over the government still.
Its less "people approve of the system" and more "people don't have any issues with the system". Anti-monarchism just isn't really a thing here because the monarchy is just... kinda bland? The most solid argument here is that it's a money sink, which is a fair point but not enough for most to protest it.
This is in very stark contrast to the UK monarchy, which does hold very considerable power and control over the government still.
Its less "people approve of the system" and more "people don't have any issues with the system". Anti-monarchism just isn't really a thing here because the monarchy is just... kinda bland? The most solid argument here is that it's a money sink, which is a fair point but not enough for most to protest it.