Compared to rest of human activity starship has a neglectable impact in environment at a planetary scale. At least they burn methane, which is better than having it in atmosphere compared to co2. I don't want to be very critical to space exploration, I follow with interest. The main point I want to refer is that using "Green" word or environment friendly to any rocket is simply ludicrous. And now Elon is endorsing a politician that doesn't care at all.
Without much research I'm almost sure, that natural methane sources, from livestock, farming are not an efficient energy extraction method, and most gets to atmosphere anyway. Why not from tundra? but again, it's likely harder, and most from remote places like Canada or Siberia, which are melting faster than usual due to decades of greenhouse effect (CO2+ CH4 and others gases...), releasing long time stored "natural" CH4 under glacier ice to the atmosphere. All due to long time buildup, and is still an accelerating process.
EV are far from being a solution or either green. The issue is really why each individual need a car at all. It's human nature, and that's like an utopia. Even if all poorest people in earth would have EV's the impact is still really neglectable at a planetary scale. It probably would be worst due to motor infrastructure needs. Still it gives good feelings to human brain like is doing is part. Yes. It helps, but not so much as one thinks, whatever production process and energy source it has.
But in conclusion, starship prototype looks more efficient in the way it uses an energy source to propel first stage. But I would not call it eco or green at all.