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."
I'm sure they named the character of Richie after Mary Tyler Moore's son, Ritchie (Richard Carleton Meeker, Jr.), who was born in 1956. Magazines of the era were fond of photos of Mary with her "two sons."
Here Ritchie is on the right, and Richie on the left.
Ritchie Meeker went to the University of Southern California, and took a job at CBS. In 1980 he died in a tragic accident while cleaning his gun.
Larry Mathews retired from show business after 1966, although he has appeared in Dick Van Dyke reunion shows. He graduated from UCLA in 1976 and went on to a business career. I can't find any photos of him as a young adult, but here's one from 2004.
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