Its really like anything else in the current situtation that is against the torah, How does a frum person run the government over non frum people.
Issues like shabbas buses, Toeivah Parades , Treif food , Army issues etc will constantly come up and you have to decide how to balance the Torah and the belifes of people who disagree. Once Moshaiach comes, thats different , but he is not here and you have to govern now. Forcing torah laws will not work and likely backfire.
Many choose not to put themselves in this position, he did .