Starship runs on methane and oxygen, but same deal.
They use different engines because there are no petrochemicals on Mars, but there is CO2 and H2O, so you can produce CH4 and O2 locally if you have a power source (presumably solar or RTG).
They use different engines because there are no petrochemicals on Mars, but there is CO2 and H2O, so you can produce CH4 and O2 locally if you have a power source (presumably solar or RTG).
So far, there has not been public information about what they're going to do about it.
A render of the moon landing Starship showed engines higher up that have been speculated to be used for landing and lunch to reduce the problem.
You need a lot less thrust to get off the Moon’s surface. That probably puts the problem back into a familiar envelope.
[1] To Mars and back diagram: https://www.spacex.com/human-spaceflight/mars/
However this is a problem that needs more study, the are various projects on how to quickly make a functional launch pad.