GMC is very important in romance novels. It gives the story structure. Goals make the characters seem purposeful, like a character aiming to re - kindle an old love. Motivations add depth, say a character is motivated by past regrets. And conflict creates drama, like when family disapproves of a relationship.
In romance novels, 'GMC' could potentially stand for 'Goal, Motivation, and Conflict'. The goal is what the character wants to achieve, like finding true love or getting married. The motivation is the reason behind that goal, perhaps loneliness or a desire for a family. The conflict is what stands in the way of achieving the goal, such as a rival for the love interest or personal insecurities.
One positive aspect is improved communication. When a family reprograms, they often have to talk more about the changes they want to make. For example, if they are reprogramming their mealtime routine to be more about sharing feelings, it encourages everyone to open up and listen to each other.
I don't have enough information to say for sure. It could be fiction, or it could have roots in reality that have been adapted or exaggerated for a particular purpose.
As I don't know the specific 'reprogramming logan gay story', I can't say for sure who the main characters are. But from the title, it seems Logan would be one of the main characters.