1) Government at its fundamental level is law.
2) Laws coerce people to behave in a way they would not ordinarily behave.
3) All laws should be just.
4) Justice is based on morality. (Morality meaning good/bad+obligation, aka the "ought/should")
5) Morality dictates that it is immoral to coerce someone except in the protection of rights.
6) You cannot make people virtuous by coercion, in order for a person to be considered virtuous they must choose their virtuous behavior freely.
7) As virtue declines in a citizenry, stability can only be maintained by an increase in law and a decline in liberty. Liberty is only possible to the degree you have self governance/virtue
Based on these above premises, the basis of morally legitimate government is a government whose only role is the protection of rights. Government which uses its power of coercion in pursuit of other aims is morally illegitimate. The great debate of politics should only happen within the bounds of the question "What rights to we have individually and collectively?". If a person, institution or movement does not make their argument for government action on the basis of an answer to that question, you can be assured they are acting immorally.
Legislating your morality is perfectly legitimate as it is the basis of all law, but don't ever forget that morality is what dictates that coercion is immoral except in the protection of self/others.
Definitions
Rights: Something which a person is entitled to
Virtue: A quality in a person that is considered good/desirable
Liberty: A state in which one is free from the coercion of others.
Coercion: Persuading someone to do something out of fear of harm.
Question to ponder. 1) At its fundamental level what does government do? 2) Why do we have any rights at all? 3) How does religion influence virtue? 4) How does religion influence conceptions of morality and justice? 5) Do we want liberty? How much? 6) Are any of the premises above flawed? Does the conclusion logically follow?