Eliminating space tourism completely would have no measurable effect on atmospheric CO2 levels for decades, if then. At the highest imaginable flight rate, the current space tourist vehicles under development will produce a negligible fraction of global carbon production, of no consequence for climate change. In the long run there are excellent zero-carbon rocket fuels; specifically, hydrogen/oxygen which produces only water. One such vehicle is under development by Blue Origin, Jeff Bezos’ company.
The environmental benefit of leading members of society seeing the Earth as a single entity with a thin layer of life, from space, with their own eyes, is likely to have tremendous benefits — just as the image of Earth from space taken by the Apollo astronauts had an enormous impact on environmental consciousness. As the price of a trip to space drops, this experience will inform ever larger parts of society.
Space activities have had huge positive impact on environmental policy, primarily through satellite observation. Space tourism is an important step forward in space development which can reasonably be expected to pay additional environmental dividends.
In any case, banning this or that activity, particularly small ones like space tourism, is a lousy way to protect the atmosphere. It limits freedom unnecessarily and doesn’t work. The core of the problem is that in most of the world dumping large amounts CO2 into the atmosphere is free. The solution is to charge appropriately for the privilege, providing the price signals necessary for the world’s economy to adjust and protect the environment.