France:
The Vichy French mount a stronger resistance forcing the Free French to rely more on Algerian and west African manpower to liberate France. Out of gratitude, France extends full citizenship rights to veterans and immediate family members following the end of the Second World War. Impetus for decolonization is rather less than OTL and thus France retains a significant chunk of territory in Africa.
India
No Muslim League. Pakistan and Bangladesh become a part of India.
Singapore
The newly independent government, in order to commit to racial harmony, decides to import Arab and Indian Muslim labor to their shores.
Russia
Have the Soviet Union survive.
Belgium
In order to develop the colony, the Belgians send agents to the Dutch East Indies to acquire laborers. The Indonesians in the Belgian Congo in a few decades have a demographic presence analogous to the Indians in Fiji. The Congo remains part of Belgium to the current day.
South Africa
As part of their schizo racial policy, Muslims are considered honorary whites by the apartheid government and encouraged to settle in the predominately black parts of South Africa.
Germany, italy and Netherlands
A combination of D-Day being a complete failure and the Germans committing to using chemical weapons. The United States unleashes the first atomic bombs on Germany, killing hundreds of thousands to millions of people. During the reconstruction process, Germany brings in more Turkish laborers than IOTL. As for the Netherlands, have them retain significant portions of the Dutch East Indies. Re: Italy, have them remain neutral in the Second World War and keep Libya. Libyans migrate to metropolitan Italy en masse looking for work and have a presence similar to the Puerto Ricans in the continental USA.
United States and Canada
Don't know how to make this work.
Sweden, United Kingdom and Spain
Same here.
Brazil
Somehow the Maronites and other Christians in the Levant do not emigrate but the Muslims do. Perhaps mostly the Druze and Alawites.