Regarding politics; Islam established a means to deal with conquered peoples. They deemed these "Dhimmi" or "people of the book".
The idea is that that "Dhimmi (Jews, and Christians, and later, extended to Hindus) would be allowed to live in return for a second-class status.
Dhimmi were 'exempt' from the army, but that simply was a means of keeping them from real power.
Dhimmi had to pay a tax, and wear special clothing (to easily mark them out as being second-class). Dhimmi, when paying the tax had to do so in a demeaning fashion.
The testimony of a Dhimmi could not be used in court against a Muslim.
Dhimmi were not allowed to 'seek converts'. New churches were forbidden and restrictions were placed upon renovating/repairing existing churches.
Dhimmi men could not marry Muslim women. And a woman couldn't simply convert so as to marry, because Apostasy (leaving Islam) was punishable by death.