The [[LGB][T]] issue isn't a simple one to hash out with any sort of universal agreement, for sure. At best, it seems nuanced.
Those who know me in meatspace for the most part seem to think in terms of me "becoming a lesbian" in the process of transition (a bit of a simplification, as I'm not violently opposed to male companionship and wasn't before, but I digress....). I was miserable and borderline inept as a "straight guy" but seem to have become quite comfortable in my skin as a trans dyke already.
My understanding of gay rights movement history is that transgender individuals (trans women in particular) were absolute leaders in making the whole thing as we understand it today happen at all.
So for at least a few reasons, I can see there being some interconnection between the two sets.
But there is definitely something to transsexuality that is distinct from sexual orientation.