New Delhi, June 1 -- One of the country's messiest and most consequential governor's races is hurtling toward an inflection point on Tuesday in California.

Voters are looking for a replacement for Democratic Gov. Gavin Newsom, and their decision will help determine the future of a state government that is a testing ground for progressive ideas and a punching bag for Republican President Donald Trump. California is not only the nation's most populous state, it has one of the world's largest economies and is home to Hollywood tastemakers, Silicon Valley disrupters and Central Valley farmers.

The race was upended in April when Rep. Eric Swalwell, who had been consolidating support among establishment Democrats, was accused of sexual assaul...