I understand that the Prophet's body of believer is to be One, just as God is one. Does this extend to all matters of politics? In other words, is it a requirement that Muslims, say, vote for a single candidate for political office?
To what point can diversity of political opinion still square with oneness of purpose within the faith?
Good question(s)!
The answer will depend on a number of things. Firstly, whether the question is being asked in context of an "Islamic" state, or a Muslim-majority state, or Muslims living as a minority.
In the first case, politics is seen as a way of going about achieving the goals and purposes of the Islamic state, which is to legislate by what God has revealed to us and to apply that legislation. Muslims would be united in that (abstract) goal, but of course can differ in the methodology of achieving that. So a difference of opinion is definitely tolerated in this matter. When the second caliph of Islam died ('Umar) there was an election committee of 6 people who went around every household asking for their opinion about who was to be the next caliph. If no difference of opinion was to be tolerated, then this exercise was foolish.
For the second case, outside of efforts trying to bring in a system that legislates not by human will but by what God has revealed to us, Muslims abide by whatever political system is extant, and vote based on what they think is most beneficial for the country. Of course different people will have different opinions.
For the third case, again, Muslims vote based on the issues and in the manner prescribed by the extant political system. Of course, it's always good to have an organized effort that analyzes the candidates and their positions and suggests strategic voting, but by no means do they have the authority to make it obligatory.
According to Shi'a Islam, only the Caliph has the right to decide about politics. The Caliph can only be selected by God; voting is not acceptable in matters of politics.
Quran 6:57 says:
إِنِ الْحُكْمُ إِلَّا لِلَّهِ
"The command rests with none but Allah:"
(The word حکم (command) in this verse has same root and meaning of the word حکومت (government).)
This remains true only if Allah directly governs people or if Allah himself appoints the Caliph to govern people. If the people select a Caliph, then this verse is no longer valid because in that case command is for the people who selected the Caliph. (I.e. command is for the voters, which is not valid according to the Qur'an)
Quran 2:30 says:
"Indeed I appoint Caliph on earth"
إِنِّي جَاعِلٌ فِي الْأَرْضِ خَلِيفَةً
In this verse, the exact Arabic word for Caliph is used. If God appoints a Caliph, did He appoint the Caliph after the prophet, or did he leave it for people to select it by voting?
Caliph literally means deputy. It is the representative of God on earth for political leadership of the Islamic government.
