I'll take from my timeline,
setting down Root, and say some Butterflies from the previous mention stuff lead to Taft not being unavailable and choosing to go on the Supreme Court in 1906. This leads to Bryan in 08 over a very conservative Republican who is chosen when Root waffles due to health. Teddy Roosevelt wins in 1912 and serve two terms.
Teddy Roosevelt doesn't find much need to be interventionist, sunsun like in my timeline there is no European War, but gets involved a little in Mexico. He isn't the racist Woodrow Wilson was so well there is an incredible movement in civil rights there is some as black troops, perhaps to Roosevelt surprise, wind up being the heroes of the small Mexican intervention. General Pershing is part of this and supports the Buffalo Soldiers under his command.
Come 1920, Democrats have still been out of office for all but four of 24 years and they control the House and Senate by now. James Cox wins the White House with Franklin Roosevelt as his vice president. Roosevelt has not been in the cabinet in this timeline but in his late 30s has been in Congress because of these butterflies. Cox is assassinated by an anarchist and Franklin Roosevelt becomes president in 1922 ironically the same way Teddy had. FDR, as he is known, is a supporter of equal rights and therefore makes the Washington DC area even more integrated then it had been, and this is helpful because there is no Wilson to roll things back. His Progressive policies allow for more improvements, and while there is lots of consternation among Southerners, especially after Roosevelt insists on federal intervention to help blacks in the Mississippi area in 1927, Roosevelt is popular enough that while he chooses not to run in 1928, the Democrats still win, albeit with a much more conservative yet not horribly racist presidential candidate, 7 term congressman and member of the Cox and Roosevelt cabinet Cordell Hull, who had the unfortunate experience to be president during a major recession, leading to many people making him the butt of jokes claiming America had gone to Hull. He did not roll back the advances in civil rights, what few there were, because of his relationship with FDR.
Meanwhile, because of the support of Franklin Roosevelt the New York Giants in 1921 had signed the first black player as a response to the Yankees grabbing Babe Ruth from the Red Sox. The integration of baseball begin slowly in the 1920s but picked up steam quite a bit as everyone wanted to compete against John McGraw.
Black Jack Pershing wound up running for president with the Republicans in 1932, with the support of Teddy Roosevelt, who was now over 70 and a senior Statesman. Pershing wound up serving two terms and America slowly grows out of its economic crisis. Pershing support of integrated military forces had grown from his time with the military since the intervention in Mexico and he used that to again slowly push civil rights forward.
I'll leave someone else to do more of America, but American society is slowly becoming used to black people working alongside whites in some areas, especially with the popularity of baseball