If there is nothing wrong in living and working in a Non-Muslim country, then there is nothing wrong in voting for that country. Voting is a right. There is no reason for a Muslim to refuse this right which is given to him/her by public’s will. Muslim’s are not commanded anarchy, they are commanded to use their minds. Allah the Almighty says:
“(…) He will place disgrace upon those who do not use their minds.” (Jonah 10:100)
Muslims who live in a Non-Muslim country can vote for a Non-Muslim candidate whom they think may provide better safety and justice for them.