The LGB and the T are fundamentally unalike, and lumping them together is forced teaming that benefits the T to the detriment of the LGB. The LGB are same-sex attracted people; all we ask is the right to pursue consensual adult relationships with other same-sex attracted people without being harassed or ostracized for it. The T are individuals who, for various reasons, wish to be the opposite sex (or, in some cases, an imaginary third sex). For better or worse, this is an impossible wish; humans can no more change sex than we can change species. Same-sex attraction is a normal variation on human sexuality, documented around the world and throughout history. Although trans activists like to point to third-gender categories in various traditional cultures as proof that "trans people have always been here," the fact is that nothing like modern transgenderism has existed until very recently. It is a culturally-bound syndrome—as Carl Eliot eloquently puts it, "a new way to be mad"—whose existence is inextricably connected with sexual paraphilia. Show me a "trans lesbian," and I will show you a man who is sexually aroused by imagining himself as a woman, often in breathtakingly misogynistic ways.
(Don't believe me? Read _Females_ by Andrea Long Chu.)
Trans "rights" are at best orthogonal to LGB rights, and often diametrically opposed. Kids who are extremely gender-nonconforming in early childhood often grow up to be gay or lesbian; nowadays, this kind of gender nonconformity is liable to be taken as "transness," meaning that children who would become healthy, happy gay men and lesbians are instead herded toward sterility, sexual dysfunction, and pseudo-heterosexuality as "trans girls" and "trans boys." Trans ideology also erodes the LGB community from the other side. The majority of transitioners are opposite-sex attracted, meaning that they become "trans lesbians" and "gay trans men," who then demand inclusion in LGB spaces and throw fits when lesbians don't want their female-identified penises/gay men don't want their male-identified vaginas.