The Rs were the compassionate conservative party of William Howard Taft, whose son Bob Taft was a moderate Republican in OH. Up until the Nixon and Goldwater days, the Rs were the people's party and put in place Antitrust provisions, so that Businesses dont monopolize ecommerce.
This would come as a hell of a surprise to the Populists in 1890s. Throughout this period the Democrats were the ones taking the lead on opposition to monopolies as a extension of the tariff issue, which they credited as helping preserve them while free trade would break them up. Cleveland had already passed the ICC as was earlier posted.
The reason that Harrison did that was the same reason that Bush passed NCLB or Medicare Part D, co-opt a policy from the other side and use it to gain favor with key voting blocks. Republicans dependent on winning working class voters scared crapless that free trade Democrats from the South were coming to dismantle their factories and their jobs along with it. However, such fearmongering only gets you so far and with the growing opposition building to trusts and monopoly, Harrison and Sherman were trying to get ahead of an issue that could give the Democrats and/or the Populists a wedge against them in their base region. It is the same reason why they moderated on the silver issue during that time period (remember Harrison had added several states to boost his reelection chances, which would have favored Silver and later backed WJB).