WASHINGTON—In the summer of 2016, FBI Agent Peter Strzok had just wrapped up the investigation into Hillary Clinton’s use of a private email server and was embarking on a probe into Moscow’s interference in the presidential election. As he watched the Republican National Convention and scanned intelligence reports and news stories, he made clear how he felt about his new target: “f*ck the cheating motherf*cking Russians,” he texted in late July. “Bastards. I hate them.”

“I think they’re probably the worst,” texted Mr. Strzok,...