Pride Glasgow say they were due to appear on the Riverside Show on STV Glasgow, but when they suggested that the drag queen appear, the show's producer refused.
The station claim that is not their understanding of what happened, but Pride Glasgow boss Alastair Smith has withdrawn from the show completely.
Mr Smith said: "We had suggested to them that a drag queen come on the show to promote the gay pride event, but they said that they didn't want young children asking what a drag queen is.
"It was really insulting. Basically they're saying they want to do a feature on gay pride without actually mentioning anything gay. It was just a bit odd.
"I've now asked them to stop any interviews with myself or anyone else connected with Pride Glasgow from appearing on the show. We've pulled out all together.
"I'm now considering writing to their chief executive to complain."
He added: "It's just absolute nonsense, children who ask questions grow up to be the well-informed, open-minded adults of the future.
"They're already used to seeing panto dames and other drag queens on TV, so I don't understand what all the fuss was about."
A post on Pride Glasgow's facebook page about the show's alleged refusal attracted more than 80 comments.
Steven Agnew wrote: "Ridiculous in this day and age. Even in the 90s, when things were less tolerant than now, we had Lily Savage presenting the Big Breakfast when kids would be getting ready for school and no one cared."
Lauren Chappell also posted: "STV should be ashamed! I'm only too happy to explain to my children what a drag queen, cross dresser or transsexual is, or anything else they may ask about. Ignorance only breeds prejudice."
While Vikki McLaughlin added: "Oh my STV! Heaven forbid children ask questions and then grow up to be open minded and accepting of anything outside societies "norms" of gender binary."
Mr Smith added that he has since emailed the show's producer to complain and ask for details of his line manager, but has received no response.
A spokeswoman for STV Glasgow said: "This is not our understanding of the correspondence with Glasgow Pride. STV Glasgow was keen to host Glasgow Pride on The Riverside Show and invited them on to promote this weekend's event."
The Riverside show is on STV Glasgow every weekday at 6.30pm. Its website says it aims to "celebrate the best of Glasgow and the West".