What occurs politically when someone converts to Islam?

Answer 1

With the exception of Israel, Lebanon, and Iran (et al.), where different citizens have different responsibilities to the state based on their religious affiliation, converting to Islam either has no political effect (this is the case in most Western countries and Latin American countries), is simply a change in official religious registration (most Islamic World countries), or simply changes interpersonal relations in a clan system (most Sub-Saharan African countries and India).

ISRAEL - Life-Cycle Rituals and Military Service
In Israel, since life-cycle rituals (marriage, divorce, funerals, etc.) are run by the clergy appointed by the state, as opposed to secular institutions, registry with the government is necessary in order for the proper clergy to be solicited for these rituals. Similarly, military service is required for Jews and Druze males, but not required for Muslims (aside from Circassian males), so conversion prior to age 18 would need to be provided to the Israeli government to avoid military service if you were a Jew or Druze male prior to conversion.

LEBANON - Political Roles
Lebanon is a Confessionalist state where individuals in a society have different political rights because of which religious community they ascribe to. As a result, which positions in the government a person can run for is completely dependent on that person's religious identification. The positions in Parliament are set where the President must be a Maronite Christian, the Prime Minister must be a Sunni Muslim, and the Speaker of the Parliament must be a Shiite Muslim. The Parliament itself must also be divided 50-50 between Muslims and Christians. As a result, if a Maronite Christian were to convert to Sunni Islam, he would have to notify Lebanon in order to disqualify himself for the Presidency and qualify himself for the Prime Minister-ship.

IRAN - Voting Permissions
There are a number of countries, like Iran or Cyprus where minority religious groups have specific legislators who represent that religious group. For example, Iran has one legislator to represent the Armenians, one to represent the Assyrians, one to represent the Zoroastrians, and one to represent the Jews. In order to vote for one of the candidates for these minority positions, you need to be registered as that minority. If you convert to Islam, you will be thrown into the general pool of remaining legislators.

WESTERN & LATIN AMERICAN COUNTRIES - Null Effect
The conversion simply means that you will attend a mosque. There is nothing that involves the state.

ISLAMIC WORLD - Identification Cards
Most countries in the Islamic World list the religion of a person on their passports and identity cards. A person who converts to Islam in the Islamic World needs to go down to the identity card office to change his religious affiliation on the card. However, this has minimal importance in actual government activities.

SUB-SAHARAN AFRICA, INDIA, AND SOUTHEAST ASIA - Interpersonal Clan Relations
In a lot of countries in the third-world, religious identification is often synonymous with clan or tribal affiliation, so while there is no governmental involvement in religious conversion, oftentimes a convert will have to leave his prior community and move into an Islamic community because of how people will treat him.