This question would be best relegated to
r/islam, but I would try my best to answer it.
Islam has 2 primary sects, Sunni and Shi'a, together they form the vast majority of Muslims.
Sunni are by far the largest sect of Islam, approximately 90%, and are spread throughout the world. Shia are the remaining 10% and are located mostly in Iraq and Iran, with minorities grouped together in various other countries.
There is not much difference in theology for both sects, and the rules of Islam are more or less the sane for both sects. There is no "liberal brand" and "conservative brand" of Islam. Islam is just Islam. It's the people who are conservative and liberal.
Now, Islam is highly concentrated in countries that are predominantly conservative, like the Middle East, North Africa, South Asia, etc... Notice how these countries are either poor or were poor in the last 50 years. Which is why Islam is predominantly conservative. You can find conservative Sunnis in San Fransisco and liberal Sunnis in Saudia Arabia.