There's virtually no crossover. Sexuality and gender identity are as related as gender identity and race, or race and sexuality. In the broadest sense you can look at oppression of minorities in general and cobble together some kind of link with that but it's extremely vague
The rights and issues of trans people seem entirely different to the rights and issues of gay, lesbian and bisexual people that it seems strange they're now represented as a single group. The result of which means that issues affect LGB people simply aren't on the agenda any more. There should be, but isn't, national strategies on sexual violence, domestic abuse and drug use that hugely disproportionately impact LGB people. Yet you'd think these last couple of years the only issues was the misgendering of Sam Smith or the Tweets J.K Rowling.
Sexuality and gender identity are no more natural bedfellows than race and ageism or female emancipation and disability rights.
If someone asked "Wait, why is it considered the Women's and Disability Rights movement?' it would be a fair question, especially if it meant the discourse surrounding the 'community' of women and disabled people became dominanted by just one group.
Issues that impact LGB people have been taken off the table for the last two or three years now. That's not to say trans issues aren't equally important. But they're entirely separate issues and separate concerns.