Much of the Left is socialist. They believe that capitalism has created most of our social, economic, and ecological problems, and none of the problems can be solved while capitalism exists. The means of production must be wrested from the rich and given to the workers who will organize it democratically and fairly. The workers will solve all our problems, but only after capitalism is entirely destroyed. Capitalists will commit any amount of violence to keep their ill-gotten spoils, and the workers will have to use violence in self-defense to win.
Many Greens are not that kind of socialist. We want to believe that we can create a government and society that will do the right thing without violence. It's worth a try. We believe that businesses must be small enough that they cannot dominate the nation and the world. So big businesses must split up so there will be more competitors and none of them too big. Much government should also be more local. Banking must be under more social control, and more local. With strong local governments and strong local economies, local areas can create local socialism if they want to, with a variety of approaches that other localities will be interested in observing.
We aren't at all sure how to solve all the problems. But local governments can respond better to local conditions, so they have a better shot at it. And if we try lots of things we can notice which work better and try them more places.
Why is this controversial? Because if it's true that nothing else is worth doing until capitalism is entirely destroyed, Green Party attempts at half-measures will fail and are not worth doing. To do that democratically, we must put our entire effort into convincing the public that capitalism must be destroyed. Anything effort put into other Green issues is necessarily wasted. Given this fundamental belief, there can be no compromise.