I will point out really quickly here that “Muslim” and “Moro” are really the same thing. So you don’t need to use both terms :). Non-Muslim and non-Christian Mindanaoans are called Lumads.

I think this is actually pretty straightforward to answer. I actually don’t consider the Filipino-American War to have ended in 1902, like, say, Wikipedia says, for exactly this reason. I put the end date at 1913 because that is when the Moros and Lumads were finally defeated and incorporated into the Philippines. Basically, the fighting continued because the Americans could not defeat the Moros definitively until 1913. That’s not to say that it was necessarily a close war. The Moros were generally in a bad position but fought to the end anyways. They had only been under tenuous grasp at best by the Spanish (or not really much at all in Sulu’s case) and the Americans were making a forceful attempt to unite all the Philippine Islands under their control. This directive came pretty early in the American invasion of the islands, and the imperial actions intensified particularly in 1899 and after. The war overall was kind of fractured. The Philippines was obviously not a united country, and Emilio Aguinaldo was not commanding the Moro and Lumad fighters. When he surrendered, that was not their surrender. So they kept fighting. American claims of sovereignty provoked resistance, notably in Sulu, where fighting lasted from 1903 to 1913.

If you are interested in going further into this topic, you should try to find a copy of The Filipino-American War, 1899-1913 by Samuel K. Tan. It actually has a very significant focus on Mindanao and Sulu since those areas are often ignored and Tan wanted to put a focus on them.