I am going to preface my answer here by saying that Pershing of course did have a paternalistic view towards the colonial subjects that he was ruling over, which was typical of most colonialism and particularly American colonialism in the Philippines. The Moro Province lasted ten years, from 1903-1913, with the capital in Zamboanga. Pershing was the last governor-general of the province. What I say here about Pershing and the Moro Province can be found in Making Moros: Imperial Historicism and American Military Rule in the Philippines' Muslim South by Michael C. Hawkins, as well as some wider politics from State and Society in the Philippines by Patricio N. Abinales and Donna J. Amoroso.

Pershing was indeed more diplomatic. He, according to Hawkins, sought a common humanity with Filipino Muslims beyond their official relationship. Pershing's time was considered the best in the province's history, and there is a plaza named after him even now in Zamboanaga (though I suppose that doesn't indicate too much, considering there are streets and neighborhoods in Manila named after objectively horrible people, such as McKinley). However, in 1911, Pershing said to a group of Muslims that he believed that the Moros should live according to the Quran because he thought that was the best book for them to follow. There may have been a feeling that Islam had prompted Moros to cultivate certain characteristics that were agreeable with modern, secular, teachings.

Pershing wrote in a letter to a colleague in 1910, "No one can be associated with the Moros for any length of time and not feel that they are superior [in terms of work ethic and industriousness] in that regard to any other Philippine people". He also repeated these sentiments to Moro gatherings, saying that the country was the country of the Moros, the strongest race in the islands, and that they should have more children to cultivate all the land in the region.

To put it simply, there isn't evidence that the claims Trump made have any historical weight, though I do want to point out, tangentially and not about Pershing, that the tactics the US used during the Filipino-American War were extremely brutal and very unnecessary. Ultimately, possibly more than 1 million Filipinos died during the first half of the war (out of a total population of only 7 million or so in the archipelago), which has several end dates but the one given by Samuel K. Tan for the war’s length is 1899-1913, and this is the timeframe I am referring to when I say “first half”. War crimes were obviously extremely commonplace (there are many conflicting accounts about the death totals among scholars, as well as different timeframes and the fact that many death tolls are referring to Luzon alone; there are varying accounts from the period and varying census data, but it is clear at least that an incredible amount of death occurred). Abinales and Amoroso mention an episode in the Moro Province where, in two major military engagements in Mindanao, American forces killed hundreds of men, women, and children. As for Pershing, however, he does not appear to be a particularly offensive figure in comparison to these other things, which is what you were asking. Though he was certainly racist, Pershing did not seem to desire being violent. However, he did impose his values as a colonial administrator: he limited the rights of the Moros (for example, they could not develop or cultivate land as they pleased, they had to go through him first) and he was a part of a policy that attempted to treat the Filipinos as a group of people needing to be tamed, so to speak; that is, policies such as forced settlement. It was also during the direct military rule that the Philippines took its modern shape, as it was only during this time that the entire archipelago became incorporated under a single government; the American military rule created the Philippine "geobody".

Despite the fact that the Americans were a dominating and oppressive force in the Moro Province under Pershing and his predecessors, it ended up being preferable in some ways to the following regime: the following years began the process of "Filipinization" (which included turning Mindanao over to Filipino rulers based in Manila), which resulted in much of Mindanao becoming ruled by Christian Filipinos. This began the process of Christian Filipinos being moved or incentivized to move to Mindanao. The Filipinization created a peace for a period of time, but it also engendered some resentment, including giving rise to the long lineage of Muslim separatist groups. Today, Mindanao is minority Muslim in large part because of this ongoing process. Today, many Muslims in the south feel that the US shirked its duty; that is, they invaded the Philippines and then left with the people in a worse position. The feeling is that the US has a responsibility to complete the project they started.