Argentina President Mauricio Macri passed a big test with global investors after his policy responses helped stem the peso’s slide and enabled the country to rejoin a popular emerging-markets index, attracting foreign capital back to the market.

But those same business-friendly stances have enraged many locals and could imperil his chances for re-election next year. Without Mr. Macri in charge, some investors say, they worry that Argentina could revert to the more populist policies that they say upended the economy and led...