Donald Trump’s decision to appear at a campaign rally for Sen. Luther Strange raises the stakes for the president in an Alabama special election that is splitting the Republican Party.

By supporting Mr. Strange in the Sept. 26 runoff election, Mr. Trump has put himself at odds with former adviser Steve Bannon, Sarah Palin and other Republicans who have called Mr. Strange the puppet of a discredited GOP establishment in Washington. Mr. Trump has joined forces with Senate Majority Leader Mitch McConnell, who has strongly backed...