As a transwoman, I can say that, yes, the transcommunity does fight and quarrel amongst itself. It's sad and embarrassing.
But we do face a ton against the non-transcommunity, especially from the right-wing who wants to make it so we can't legally identify as our identified gender, make it harder to change our legal gender marker, and even prevent us from using any public restrooms. Stories of hospitals refusing to treat trans-patients are not uncommon. If I can remember the name of it, there is even a documentary that featured a FtM who developed cervical cancer, but because he was a male, he could not get treatment for his remaining female parts, which ultimately killed him.
In terms of race? That one is still very much alive and well. While many people have gotten over it, there are still many whites who hate blacks and blacks who hate whites. And, if you notice the right-wing voter-ID laws, they are notorious for having detrimental effects on demographs that tend to vote Democrat, such as black people and college students.