In addition to what Yankee said, Sherman in particular —who was an architect of the postwar Republican economic policy as secretary of the treasury under Rutherford B. Hayes —eventually grew concerned that the pro-business policies of the immediate postwar period had gone too far and came to believe that some regulation was necessary to stabilize the market. This was the same rationale that led him to support the Silver Purchase Act which bore his name. In the same way a doctor might prescribe nicotine patches as an alternative to cigarettes, Sherman and Harrison moderated on these issues not because they suddenly decided soft money and regulation were great, but to ensure the long-term viability of the capitalist system. "The ends justify the means," as the kids are saying these days.
Was this Bismarckian embrace of regulation also a driving force behind the Republican Progressives such as Teddy Roosevelt?
To a great extent, I would argue yes, it was. Roosevelt in particular was always careful to distinguish between the "good" trusts that were a force for societal and economic progress and the few "bad" trusts that used unethical tactics to eliminate competition and drive up prices. (The story about the teddy bear is actually a useful anecdote for understanding this mindset: he wasn't anti-hunting, but he believed in playing fair.) Hence despite his reputation as a trust buster, he actually prosecuted fewer trusts than either of his immediate successors; one reason for his primary challenge to Taft in 1912 was actually that he believed Taft had taken things too far.