When she was raped at gunpoint at the Alexandria, Va., pool where she worked in 2016, the 24-year-old lifeguard could describe her attacker only as a thin man she believed was 35 to 40 years old and a little over 6 feet tall. Three years later, police arrested Jesse Bjerke, after having DNA from the attack analyzed by genealogy researchers who used public databases to link the sample to people in Bjerke’s family — an increasingly common tool for cracking unsolved crimes. Bjerke is also under investigation for a similar rape at a pool in Fairfax County in 2015, according...