Yes and no..
Firstly, the T in LGBT doesn't just stand for 'transexual', it also stands for 'transgender' (nowadays, I would argue it's much more correct to associate it with 'transgender').
There's a fairly important difference in that transexuals consider themselves to literally be normal men/women who have somehow been born with the wrong sex, and would generally deny any association between what they are and any other form of sexual "deviance". Many transexual people find the LGBT label offensive because they see it as a recognition of the insincerity of their claims.
Transgender is a much more nuanced term which encompasses a much wider range of positions. That's not to say that most transgendered people don't utterly see themselves as functionally members of the "opposite" sex, or that they don't often feel considerable body dysmorphia, but they accept that sex can be a little more complicated than the above description implies. I don't want to generalize, because it's quite possible many trans people still use the terms interchangably, but there tends to be a feeling that a person can want to change their body or their social gender identity without their being some giant cock-up of nature involved.
Secondly, there is no clear line where gender non-conformity becomes transgender. Unlike being 'transexual', a transgender-identified person doesn't need to be diagnosed with a gender identity disorder and doesn't need to commit to having surgery (although again, many do
) changing your gender does not require you to have surgery or physical body alteration, so there's no real line or easy way to tell the difference, for example, between a stone butch lesbian and a "pre-operative" (I hate that term) female to male transgendered person (transman).
The reason I've bought this up is that this similarity also caused enormous tension sometimes. There has been an awful lot of fighting it out between these two communities over what qualifies a person to be one or the other, because despite being relatively indistinct to an outsider they also tend to see themselves as being very different. So yes, there can be a lot of posturing and mutual dislike over these things.
Thirdly, and I've hinted at it already. The real reason for including trans is that the general heterosexual population tends to lump every form of gender non-conformity together. There's no real line between homophobia and transphobia, any non-heterosexual identification in our society is open to an abusive response simply for not being "properly" heterosexual. We all suffer variations on the same social consequences regardless of whether we're gay or bisexual or trans, so we all campaign together against it.
Let's also break down what the LGBT community is, because it often seems to imply some kind of hive-mind which doesn't exist. When we talk about it in these big monolithic terms, what we generally mean is the pride movement, or rather the legacy of the pride movement (the movement itself isn't acknowledged so much). The pride movement, despite the outside perception that it's a very homogenous 'gays only' thing, is incredibly accepting by design. I've seen heterosexual people in the BDSM scene march at pride holding hands, noone cares. The pride movement remains largely committed to a very gay-liberation agenda, and that is to combat the completely monolithic role in our society and media of a very specific and "normative" type of heterosexual identification which is exclusive and hostile to any non-conforming alternative to its very rigid idea of gender distinction and complementarity.
Arguing for the right for gay men to be considered as "real men" (or more broadly for the whole idea of "real men" and "(un)real men" to stop being so fucking important) is really not that different to arguing for the idea that someone born male can be a "real woman" or vice versa. There is a huge amount to gain from the collective association.
I won't deny that many people on the ground outside of the pride movement and its events don't always see it, but I think if you dig into the politics of it you'll find that a lot of the conflict is about representation, and in that sense you'll find a degree of resentment amongst just about any group apart from exclusively gay man (who are enormously over-represented in LGBT politics). Most bisexuals feel that gay men don't really understand them, a lot of lesbians feel the same.
I think very few people would suggest that this erases the value in having an umbrella under which people can take shelter and campaign, as long as we all remember to step out from under it sometimes.
To be blunt, I know several transgendered people. Any intollerance they may have suffered in the "LGBT community" pales in comparison to how most heterosexuals seem to think of them and react towards them, so for the most part they are very grateful, though certainly not without reservation. That said, the "LGBT community" is not a homogenous culture - in terms of places to go, things to remember and internet presence, trans people very much have their own separate communities. As with all things around this issue, there's considerable overlap, but you don't see tons of poor trans people hanging out in villages and gay clubs looking bored and being casually insulted by passers by.
