Every organization has the right to limit its support and its membership to those who profess and promote the organization's goals and teachings. Why should any organization allow a group to use its name, its facilities, its funding, etc. to promote an agenda that is not espoused by the organization?
Would any LGBT organization like it if some group were to use their name and funding to promote a gay reversal therapy or other any other agenda aimed at undermining their goals. I really don't think so.
The current teaching of the Catholic Church is that homosexual behavior is intrinsically disordered and as such is not a gift. That is its teaching and it has every right to teach it to its members no matter how wrong we may think it is.
As a lifelong Catholic who knows very well the teachings the Church, I left my Church and faith because I could not accept its teaching that I am somehow disordered and need to be fixed. A day will come when the Church will see a way in which to expand its moral teachings to include members who express their sexuality differently from the majority and it will do so or fade further into the insignificance of the distant past.