Not just lay communities, but I have always envisioned a secular institute, as well. Some secular institute members are required to maintain confidentiality where membership is concerned. Such might be the case here.
All new charisms begin as their own third orders, though, which is what you’re talking about doing. Start as a lay association (which one person can do), and see where the Holy Ghost takes the members.
Whatever is done would definitely fulfill a need, which is the first requirement for starting something.
The picture of Marie Mediatrice has a rainbow. I have used that pic to post a novena for the LGBT community. I have also always encouraged celibacy (also known as ‘asexual’) for the sake of the Kingdom of God among the same group.
Another thing to keep in mind is that the ultimate occultist is an active homosexual. The only persons on the planet who need to be thinking about sex, and in its proper form, are one man and one woman joined in holy matrimony. Everyone else needs to imitate the angels.