To set the stage here, I really wish I could say "Oh, it'll be easy, because almost all gaming groups are friendly and inclusive!" Sadly, that is not the case, which is why I'm not going to recommend that you start with generic online group-finders. I do think, though, that there are definitely plenty of inclusive RPG players out there! In fact, you may already know some who haven't mentioned it, so I suggest exploring that first - see below.
As for where I'm coming from: one of my best friends is NB and likes playing NB characters, so I'll share what I've learned from forming 3 different groups with them, as well as from my current "college group": me, a friend in Iceland, and a friend in New York who actually went to college together, plus two people my NY friend met there (including an NB playing for the first time). I guess theoretically the three of them could be in the same place sometimes, but in practice we all enjoy playing over Skype without having to put on pants and leave the house. ^__^
Start with people you already know are cool about your identity, and ask if any of them want to play an RPG. You're looking for a group of people who a) are LGBT-friendly and b) play RPGs. Based on your question, the first one is a dealbreaker, but you might be able to be a little bit flexible with the second. In my experience, it's more reliable to search the set of LGBT-friendly people for current or potential players than trying to search the set of gamers for LGBT-friendly ones. If you survey all your acquaintances, online and off, you may be surprised to find a lot of experienced players - and even if you don't, in my experience, fumbling around with good-natured amateurs is way more fun than playing with a master storyteller who's kind of a jerk.
So put the call out on your social networks (by which I mean both FB/tumblr/whatever and meatspace social groups). If you get lucky, there will already be a group you can join. If not, you can probably make one. You want about 4-6 people, hopefully including a couple people who've played before, a couple who are willing to give it a try if people will be nice, and one or more willing to take charge to the extent the game requires it (see points 2 and 3 below). Keep in mind that while it usually makes things easier, it's not strictly necessary for anyone to have experience - some games don't require it, and some others have decent starter sets to teach everyone the basics, including the GM. Go down the list from friends, to acquaintances, to strangers - not total randos, but people from supportive online communities, who are more likely to treat you with respect. Hopefully you're already in some, but one option would be Friends of Captain Awkward, and they can also direct you to others.
Another would be convention forums - by no means all of them, but some cons have a reputation for healthy and inclusive communities if you ask around. If it makes sense for you, you can actually go to one, look for panels on "Queerness in [MEDIUM]/[GENRE]/[WORK]", and see if people there are interested - lots of things grow out of after-panel discussions. If all else fails, try the general RPG matchmakers, but see my last point below.
Make sure someone fairly central to the group has your back. Some of the games my first friend and I are in, I'm the GM, and some not, but either way I know everyone and helped assemble/coordinate the game. Obviously, we only play with people I'm pretty confident won't cause a problem to begin with, but it also helps to be in a situation where I can say or imply "This is my friend, everybody's gonna be cool, right? Right, that's what I thought." In my college group, someone else is the nexus and (at least mentally) vetted everyone for queer-friendliness and general suitability. You may be able to help fill this role if you know more gamers than your friend, even if you just make the introductions and can't play yourself at the moment.
Think about the system. If you discover an existing group that you want to join, of course, it may not be up to you, but if you're starting a new game, think about it. Though principled people recognize that everyone at the table is an equal participant in the activity, the refereeing and responsibility most traditional games put on the GM can lead to ways of thinking that are, well, hierarchical, which can be good or bad. If that person has your back as above it can be helpful, but it can also present a problem if you don't know and trust the GM. Consider GM-less games like Microscope if you're worried about one person having too much power over the group. (Bonus, Microscope is shorter and easier to get into if you do have new people, and can be a great gateway to other RPGs.)
Finally, begin as you mean to go on. Once you've got what seems like a good group, don't wait until you're three weeks in to discover that one of the players is going to make your life miserable. It's likely to be uncomfortable, but to the extent you feel safe doing so, you want to draw out any unpleasantness right away so you can take action. Depending on your level of directness, you could do some or all of the following:
- Mention your identity directly and confirm that no one's going to be weird about it.
- Announce during brainstorming/character creation that you're planning on playing a queer character and observe the reaction.
- Suggest adapting the X card or other explicitly consent-based mechanics for your game, both on its own merits and to judge the reaction.
If someone balks, well, you've discovered that conflict before anyone got too invested, and they can self-select out and find a different group (or, worst case scenario, you can do so.) This will be especially important if point 1 doesn't pan out and you start looking on the broader Internet; I'd put something in your profile (which can of course be anonymous if necessary) that will weed out the bozos quickly. It still may take some trial and error before you find the right group; this is a way to get that out of the way faster.
Probably none of these (except maybe #1) will save you from people who think they're friendly but actually aren't. But all in all, I think you and your friend will be able to find what you need. Once you've identified the players, our questions about online-roleplaying should help you figure out the mechanics and address hurdles involved with actually playing. Good luck - and may all your games be free of problem-players, though we'll be here if they're not.