I'm way out of the closet. Not that I wear a rainbow flag adverstising my homosexuality. I just don't hide it. Don't talk about my girlfriend or my wife, I talk of my boyfriend and partner, etc.
I've found health care to be the most open-minded field of any I've seen and I'm very comfortable being out. When I worked in the insurance business I kept in the closet.
Can't help you with the organizations. But there are organizations for everything nowadays, or at least websites and newgroups.
I find that by being out and honest and mainstaining high profressional standards as a nurse people don't care. They want a good nurse, caring profressional, educated, safe, and helpful working with them, what you do in your personal life doesn't matter to most folks.
I don't feel it's necessary to be out to patients. Patients don't need to know about my personal life.