All human beings have a sexual orientation either heterosexual, homosexual, bisexual or asexual.
A transgender person has a sexual orientation based on their sex, again either heterosexual, homosexual, bisexual or asexual.
Historically, the linking of LGB and T was because some (not all) Transgender people (with gender dysphoria) were also homosexual or bisexual. Although historically they were not always welcomed by the LGB community.
Time has moved on and transgender now includes many people (mainly males) who are heterosexual and who have paraphilias including exhibitionism, voyeurism, AGP, pedophilia, frotteurism etc. The presentation as a TW enables them to be in female spaces where they can fulfill their heterosexual paraphilic needs.
Paraphilias are completely different to gender dysphoria but the wide spread acceptance into the transgender umbrella is the crux of the debate. It is why women, including lesbians, historically accepted TW with gender dysphoria into female spaces but now consider TW with paraphilias a threat in female spaces.
Rapid Onset Gender Dysphoria, primarily in teenage girls, is a separate but equally concerning issue. I am hopeful the Cass Review will set out an appropriate, scientific approach to protect girls from making life changing decisions before they have explored all the options.