I did the math, and the impact is not negligible. One single launch releases the equivalent of 5000 tons of CO2. Elon wants to get to the point where there are thousands of Starships, each doing a few trips to orbits per day. That would be more than one millions launches per year, or more than 5 GT of CO2-equivalent. That's about 10% of the worldwide emissions today.
One million launches per year seems to be adequate trade for 10% global emissions. This level of technology implies we are able to reduce emissions elsewhere.
I think it’s ludicrously optimistic to think that this would substitute for reductions elsewhere. What possible
mechanism could reduce 10% of global co2 emissions when many of these launches will be tourists and starlinks?
1 million launches per year implies at least a decade or two of development. There is a lot that can change in that time - for example energy production can move towards renewable and nuclear. Few decades more and we might get fusion too.
The limiting effect for Starship launches won't be CO2 (direct air capture could counter that), it's injection of water into the stratosphere. Ballpark I think the limit would hit at about 100,000 launches/year.