And ads for Randy Minchew, a former Republican delegate aiming to retake his old seat in Loudoun County, northwest of Washington, say he favors “stronger laws to keep guns out of the hands of those who would do us harm.” Mr. Minchew carried an “A” rating from the National Rifle Association in each of his last two campaigns.

Mr. Sturtevant, Ms. Dunnavant and Mr. Minchew each declined to be interviewed.

“We’ve come a long way in Virginia that the Republican Party is trying to run on Democratic issues,” said Terry McAuliffe, a Democrat who was governor from 2014 to 2018. “These are the same cats who fought me on Medicaid, who fought me on guns, on the environment and on women’s issues every single day.”

Republicans remain split on how to define themselves. John Whitbeck, a former state Republican chairman who resigned in protest when Mr. Stewart won the 2018 Senate nomination, said the party was adapting to a changing Virginia.

“When you have a state that is transitioning to light blue the last few years, the Larry Hogan Republican brand has a better chance of success in the suburbs,” Mr. Whitbeck said, referring to the moderate Maryland governor.

Mr. Stewart, in an interview, dismissed the attempts to appeal to Democrats as doomed to fail.

“It’s never worked. It never will work,” he said by phone from Hawaii, where he was vacationing before the election. “You can’t win by abandoning your base and trying to outflank the Democrats to the left. It amounts to political cowardice.”

Today’s Republican Party of Virginia is aiming to have it both ways. John Findlay, the party’s executive director, said its base voters “understand that maybe if there is something that I disagree with, it pales in comparison to where the Democrats want to take us.”