How would the world be different if Muslims had colonised North America instead of the English?
It depends on which Muslim group though, but it's likely to be Turks (not just the Ottoman/Osmanli Empire, but also other Turkic dynasties), given that they dominated the Arab World and Iran. South Asian and Southeast Asian Muslims could also be the ones who colonized North American, but let's just assume it's the Turks.
In my version of the story, the Ottoman/Osmanli Empire somehow made its way to North America, which is not easy because they had to get through Spanish and British naval power. Assuming the Ottoman's naval power was comparable to Britain and Spain, they reached their way to North America, while Mexico and the rest of Americas were Spanish-controlled.
Like the Europeans, the Turks accidentally brought disease to the Native Americans, which wiped-off much of their population. Turks began establishing settlements and exploited the natural resources. Native Americans were slowly Turkified like the Turks did to Byzantine Christians, and non-Muslims were given additional taxes, causing a steady conversion among the Natives.
At some point, they rebelled against Mainland Ottoman and established a new country called the United States of America. Their official language is common-Turkish instead of Ottoman-Turkish, which was only known among the educated and privileged. In its later decades, they received immigrants from different nations, with majority from Turkey and Middle East. Thanks to its population and European technologies, it easily outpowered European countries in the beginning of the 20th century, rivaled by the Soviet Union.
During WW1, USA didn't intervene with the war and Germany didn't attack USA because USA was on Ottoman's side. In WW2, USA helped defeated the Nazi alongside with Soviet and the Cold War began. USA would be perceived as ‘Savior of Islam' since communists often ban religion. Many South Koreans converted to Islam instead of Christianity due to contact with US missionaries.
USA might never support the establishment of Israel and 9/11 would most likely not occur given that majority of Americans are Muslims. During the Gulf War, the US still helped Kuwait and Saudi Arabia from Iraqi attack, but didn't receive the same backlash from Muslims as the real USA due to religious similarity. USA might still support Iraq during the Iraq-Iran War because the new Iranian regime was hostile towards the Sunni USA.
New York would be called Yeni Ordu. Washington DC would be called Mehmed DC (Name of the first US president). Los Angeles might still carry its Spanish name. The White House would look like the Hagia Sophia Mosque. Las Vegas might not exist given that it's prohibited in Islam, but let's just say the Muslim US became as secular as the current US.
Instead of churches, there would be mosques everywhere. Instead of African slaves, they brought Eastern/Central European slaves. Instead of hamburgers and hotdogs, there would be kebabs and other Turkish/Middle Eastern/North African cuisines modified to suit local taste. And ofcourse, they're halal.
It would still be the same under a different religion... they would have killed the Indians calling then a race of Satan ... and there would be still be racism. A Religion that travels bring death with it were ever it goes ...