One area I am confident we will not see a difference in is complete silence/acquiescence regarding the Japanese annexation of Korea. Like Taft, Theodore Roosevelt would see absolutely no reason for the US to stick up for Korea with Korea not demonstrating much ability, or in his view, effort or talent, for sticking up for or developing itself.
On domestic matters, Theodore Roosevelt would probably be facing a more conservative Republican Congress than his personal inclinations.
I wonder if he nevertheless tries to push progressive legislation their way that is more than they are comfortable with, and if the Republicans in Congress face the strong setback in the midterms which lost them both houses of Congress in real-life 1910.
In American racial policy and politics he might be more positive in a very, very small way than Taft, assuming he continues his personnel policies in a linear manner from his previous term and three quarters in office. He departed from prior Republican practice by *not* reserving certain federal patronage appointments, in the north, south and DC for African-Americans, that had traditionally become reserved for African-American Republicans since Administrations in the Reconstruction era. Seeking to attempt to gain a white constituency for Republicans in the south, he discontinued this tradition and opened up these appointments to all candidates as incumbent appointees retired or died, usually resulting in selection of white men. He wasn't purging or firing black federal officials, but their presence in federal bureaucracy started to decrease through attrition during his OTL terms.
Taft continued the no reservations and attrition policy, but also hastened to suspend federal officials, usually black, whenever local constituencies made a controversy about it and went through an open reappointment process. This quickly taught southern constituencies they could usually get African American federal appointees ousted just by sending enough letters of complaint to Washington. This decimated the rank of African-Americans in civil service in the south, before Woodrow Wilson purged the remains.
Theodore Roosevelt might not encourage mass complaint and turnover by giving in so easily as Taft. Then again, he might, since he did openly say he saw whites as the more important constituency to pay mind to from a political point of view.
