I' m left-handed but I would never think of identifying myself as being part of some diffuse group of people 'united' by handedness. In the same vein I do not see why gays, lesbians and bisexuals are to be seen as part of a single group given that as far as I gather there is often not that much love [no pun intended] between the former two - it is not as if gays and lesbians have much in common.
Do you truly identify as 'an LGBT person' - implying that those who claim to be spokespeople for 'this group' also speak for you - or do you just see yourself as a gay, lesbian or bisexual man or woman? Or, to put it even more bluntly, would you not rather see yourself as a person who happens to be gay or lesbian or bisexual, just like I see myself as a person who happens to be left-handed? I may sometimes grumble about some object which could have easily be made to fit left- and right-handed people alike [1] but I would never join a left-handed political action committee, nor would I trust anyone to 'speak for me' in such a context because I don't want to be used as a pawn in some ideological/political struggle.
[1] If you ever start a cheese packing facility make sure to put a peel corner on the left and right hand side of the package, the latter is far more useable for left-handed people...