Re: adopting an LBGT kid. Unfortunately, as someone who was involved with helping a friend with the fostering process, I learned that you actually can ask specifically for a LBGT kid, well, kind of. When you go to websites and look at the list of kids available, you'll notice that some of the kid's profiles will say "This child would prefer his/her foster parent to be LBGT friendly". If that isn't enough, the other issue is that some of these kids you can just TELL are LBGT. Lots of kids wearing trans or lesbian badges in their photos, etc.
Check it out yourself on this website:
https://www.adoptuskids.org/meet-the-children/search-for-children/search
That's the main website people use when considering fostering/adoption. Read their profiles. Some profiles are more filled out than others, I did a casual search just now and already found a LBGT kid.
Not only can you figure out which kids are LBGT, If you read between the lines, you can also figure out which kids have been sexually abused and has behavior problems, etc. You can also search by disability, and find yourself a kid that is non-verbal or completely dependent on caregivers. Unfortunately, abusers can and do use this site to pick their victims.