Re: Martian settlers
US citizens who live outside of the US (“outside” includes Mars, since the US is a state party to the Outer Space Treaty) retain their right to vote in US elections as long as they hold US citizenship; their votes (via absentee ballots) would be tallied according to the jurisdiction of their last residence within the US.
It would be far more interesting to see residents of the District of Columbia throw their own Commodity Party, since they pay federal taxes but haven’t had voting representation in Congress since 1801. (As a result, US expatriates on Mars who last resided within the US in DC would remain without voting representation in Congress.)