Even in deep-red states, voters embraced an array of liberal-backed ballot measures in Tuesday's election — expanding Medicaid, targeting gerrymandering, boosting minimum wages, legalizing marijuana use.

The results heartened left-of-center activists, who see a path going forward for circumventing Republican-controlled legislatures. With the new Congress deeply split along partisan lines, the outcome ensured that the states will serve as pivotal battlegrounds for social issues heading toward the next election in 2020.

One of the strongest messages emerging from the results is that voters are e...