Many stars of children’s television shows have become victims of internet fixation, and “Blue’s Clues” lead Steve Burns says that online rumors have taken a toll on his own mental health over the years. Appearing on Rainn Wilson’s “Soul Bloom” podcast, Burns reflected on his negative reaction to a lingering online rumor that he had died before finishing his tenure on the series in 2002.

“When a rumor like that persists for three or four years, it stops being funny,” Burns said. “When it persists for 10 years it feels like a cultural preference. … When it persists for 15 or 20 years, you start to feel like you’re supposed to be.”

Burns starred as a fictional version of himself on Nick Jr.’s “Blue’s Clues,” speaking directly to the camera (and television viewers) in each episode from his first appearance in 1996. He was the inaugural lead of the series, appearing in...