I suppose it could depend a bit on how secure one is with oneself. If one's identity is tied to social roles (religious, family-specific, "mainstream," etc), that foundation can get rattled when the person observes someone else ostensibly challenging those roles. I could argue that a great number of institutions and media rely on people remaining insecure. Advertising generally needs TV viewers who are mentally vulnerable and susceptible to its persuasion techniques, and TV programming will often cooperate (local news emphasizing crimes, political shows that issue orders/slogans/speculation/personal attacks rather than critically considering issues, reality shows that humiliate contestants in order to attract and provide temporary satisfaction to insecure viewers). Some political/religious leaders find that instilling fear is a convenient means of suspending thought and rallying people to a desired action. These devices are quite profitable, but they are often, to varying degrees, abusive to the targets and abusive to any punchlines/scapegoats used along the way. They distract their targets by channeling frustrations against said punchlines/scapegoats while extracting money/power from the small fortunes of many people to enhance their own larger fortunes.
But then, the natural question seems to be "what can we do about it?" I'm going to bounce around some popular ideas just to get things started.
1) Civil disobedience. Disrupting public meetings or people chaining themselves to object is something that tends to draw ridicule, but the sit-ins of the 1960s are something, at least in retrospect, considered to be brave and honorable. Perhaps a reason sit-ins are looked at favorably now is that the disobedience itself precisely embodies the change people want. They sat waiting to be served at a restaurant not for the sake of breaking a rule/law, but so the restaurant would sell them food. Civil disobedience is perhaps at its best when it is conducted in this way. The restroom issue for certain TGs (unfortunately) can sometimes be a problem because *some* fears surrounding it are understandable on some level, but defying other elements where you are denied rights/service when the public is generally expected to receive them are suitable for working for change. Plus, getting your case in the court system will get the courts to deal with your issue (the "crime") rather than something unrelated, so you can possibly even work up the court system and have the law/rule thrown out.
2) Social interaction. You can talk with individuals as the matter comes up, but just being a reasonably competent example of your "group" can win some hearts. If they ask questions, give answers. It won't work with everyone you encounter, but you can probably get some relatively moderate figures to sympathize. There aren't that many voices speaking on behalf of TGs or with direct understanding of TGs, and we are in a pretty good position to do so. It's easier to hate someone without actually having to see and know them, so TGs even putting on a mediocre presentation is better than nothing.
I don't think seeking out opposing leadership and organizations will particularly help, because they will have considerable difficulty relating to your issue, and they aren't about to mess with the foundation that their empire rests on. As it is, many of them will remain impetuous even against overwhelming evidence and disapproval, and our "niche" group is not about to do any better. I think #1 and #2 are our best hope.
I wonder what other ideas people have.