HANOVER, N.H. — Rep. Dean Phillips is addressing a number of issues in his uphill, upstart campaign for the Democratic presidential nomination. But none are stirring passions on the trail like the Israel-Hamas war. Public polling shows that Israel divides the Democratic Party. It prompted a protest at the Democratic National Committee headquarters this week that ended with the Capitol Police breaking up the demonstration. Members of Democrats’ House caucus have divided and aired critical statements against each other. And in the uncontrolled environment of the New Hampshire campaign trail, where voters can come and go and air questions as...