The "Lavender Mafia" refers to an informal network of gay executives in the entertainment industry. https://en.wikipedia.../wiki/Gay_Mafia
But more generally it refers to the Catholic Church. A faction within the leadership and clergy of the Roman Catholic Church advocates the acceptance of homosexuality within the Church and its culture
A recent paper by a Ph.D. priest notes his discovery of a “huge homosexual underground in the Church” blocking justice for those abused by homosexual clergy. https://www.lifesite...in-the-church39
They know well that they may be exposed and embarrassed, so they shield one another by offering mutual support. They build informal relationships reminding of a clique or even mafia, aim at holding particularly those positions which offer power and money.
When they achieve a decision-making position, they try to promote and advance mostly those whose nature is similar to theirs, or at least who are known to be too weak to oppose them.