Damn, I thought non-golfing Australians were less anti-golf than Americans. But Sydney and Melbourne are tough with their tree ordinances! New South Wales GC has issues with the local council declaring the native areas between holes must be preserved.
To answer the question in the OP, yes, I've had a couple of consulting clients where the local township nixed a lot of the tree removal we had recommended. Those were years ago, but local tree ordinances are still a thing. They'll have more chance of overturning the politics if the trees are non-native, or can be shown to suck up a lot of water.