“To beat John Faso, you’ve got to have a candidate that can do it all,” he told the recent candidate forum. “Make no mistake about it: outwork, out-raise, out-organize and inspire real turnout. I can outwork because I come from working-class roots. And my parents taught me from Day 1 to work twice as hard.”

But some voters worry that Republicans will use the carpetbagger moniker to undermine a few of the candidates, including Mr. Delgado, should he win the primary. “It’s good to leave and see some of the world, but that was an issue for Zephyr Teachout,” said Carl Parris, 66, of Rhinebeck, referring to the Democratic candidate who lost in 2016 to Mr. Faso.

While his wife, Lacey, is from Woodstock, Mr. Delgado grew up in Schenectady, which is less than 20 miles north of the district. The couple moved to the district only last year when they bought a house in Rhinebeck. Before that, they lived in Montclair, N.J.

“This is a place where my wife and I made our roots,” he said in an interview. “My parents live an hour away. Lacey’s mother lives 20 minutes away from us. We were married in Catskill. And I was just inducted into the Upstate New York Basketball Hall of Fame.”

Other candidates have sought to distinguish themselves through policy and political support.

Mr. Beals, for instance, presents himself as the most progressive of the lot — the self-described “Bernie Sanders candidate” — with endorsements from national groups still aligned with the United States senator from Vermont.