tl;dr it won’t happen
There is some concern from solid rocket motors, whose exhaust is absolutely terrible environmentally (big clouds of toxic smoke that erode launch infrastructure, etc). Luckily, SpaceX doesn't use any of those.
[1] https://arstechnica.com/science/2018/03/spacex-launch-last-y...
[2] https://www.engadget.com/2018/03/25/spacex-rocket-carved-gia...
That is what people thought about automobiles emitting co2. If we have learned anything, we would be extremely wary of anything that causes big disruptions in the environments, how ever innocent it might seem...
Wrong. We didn't know that. We hoped the co2 will be cleaned up by the mechanisms already in place, and we thought the effect would only be temporary. Just like we think the holes caused by the rockets are temporary now, and will not have any cascading effects.
Incredibly short sighted and We have learned nothing from history if we continue to reason like this.