Were Muslims ever forced to move out from Islam?

Answer 1

Yes. Many times and in many places. When Spain was conquered, the Muslims were forced to accept Christianity or leave Spain. Thousands of Muslims were killed who refused to quit Islam. It also happens in India.

Answer 2

The question as written is confusing and there are three ways to understand the question.

Were Muslims ever forcibly expelled from their homes by Non-Islamic States?

YES. This has happened on numerous occasions. The most famous of these was when Catholic Spain and Portugal kicked out the Muslims of Iberia in 1502 and 1497 respectively. However, other incidences of Non-Islamic States expelling their Muslim populations included, but are not restricted to: (1) the re-conquest of Ottoman territory (the Austrian Empire, Serbia, Greece, and Russia all expelled Muslim populations in the areas they conquered), (2) the expulsion of the Lipka Tatars from Catholic Lithuania, (3) the expulsion of Muslims from the Sikh Empire (in parts of modern day India and Pakistan), (4) the expulsion of the Dungan Muslims from China, (5) the massacres and expulsions of the Cham in Cambodia, and (6) the recent Serb massacres/genocide of the Bosniaks and Kosovars.

Were Muslims ever forcibly expelled on account of their sect by Muslim-Majority Countries?

YES. There were a number of Islamic countries that were sectarian in their outlook and, therefore, expelled Muslims who were believed to be of the wrong sect. The most clear attempts at this in the pre-modern era were the persecution by the Ottomans of the Shiite and Alevi minorities and the persecution of the Sunni minorities in Safavid Persia. In more recent times, the persecution of the Ahmadiyya minority in Pakistan, the forced relocation of Sunni and Shiite Iraqis, and the low-level ethnic cleansing of Hazaras in Afghanistan are examples of Muslims being expelled on account of their sect in Muslim-majority countries.

Were Muslims ever forced to move by agreements between Non-Islamic States and Muslim-Majority Countries?

YES. There were several times where population swaps were agreed to between Non-Islamic States and Muslim-majority countries in order to resolve conflict, but these population swaps required large numbers of Muslims (and Non-Muslims) to leave their homes. The most famous two such exchanges were those between Greece and Turkey in 1923 and between India and Pakistan in 1947. Israelis argue that this effectively happened between Jews and Arabs in 1948, but the Arab States reject the argument that they have any duty to settle the Palestinians who left the State of Israel during the war as Israel has settled the Jews who fled the Arab World.