It was a hybrid workplace-nuclear family sitcom: Rob Petrie (Dick Van Dyke) had a job writing comedy bits for The Alan Brady Show, along with his coworkers (Morey Amsterdam, Rose Marie); meanwhile, he had a wife and son (Mary Tyler Moore, Larry Mathews) back home in New Rochelle.
Larry Mathews, born in 1955, played Richie Petrie. He was less than ten years old during the show's run, so he didn't get any teen idol attention, that I know of. Or many plotlines. The only one I remember has his parents explaining why he got the gender-transgressive middle name of "Rosebud."
Here Ritchie is on the right, and Richie on the left.
No evidence that either was gay, but Mary Tyler Moore was a strong ally.
See also: Looking for Muscle on the Dick Van Dyke Show