I feel like I should say something here.
I was on board with gay rights before I went trans, but especially since I went trans I feel a strong kindred alliance with lesbian and gay issues and people. Now, gayness, lesbianism, and heterosexuality are all variations on one theme. Transgender is another thing entirely different from all of the above. Regardless of which way your sexual orientation is pointing, gay or straight, the basic fact is that it’s about who you’re attracted to. It’s all about relating to others. Kate Bornstein in her great book Gender Outlaw noted that gay and lesbian orientations inherently build communities, because it’s all about connecting with others. Meanwhile, transgender has no reference to others; it’s about how you understand your own self. It’s inherently introspective and maybe also introverted. That’s the explanation for why there isn’t much of a transgender “community” compared with the big, vibrant gay & lesbian communities.
Regardless of the above, gay and trans are natural allies because we’re all queers. Queerness unites us. That counts for a lot. KellyM was right on target by citing the Stonewall riots as not only the defining moment for gay consciousness, but for gay-trans alliance. It was mainly trans leaders who made it happen at Stonewall in 1969. How soon their contribution to queer liberation is forgotten.
I haven’t noticed animosity between gays and trans people personally, although I’ve been involved with the LGBT scene only a short time. There was one tendency among some feminists to bash transsexuality, but Patrick Califia (back when he was still a female-identified butch dyke named Pat Califia) argued back eloquently against this prejudice in Sex Changes: The Politics of Transgenderism, and I think succeeded in persuading many lesbians and feminists to accept trans people. Califia has done a lot toward trans understanding, both before and after he went trans. I feel we all owe him a big debt of gratitude. As for trans prejudice against gays, this makes no sense to me whatever. I haven’t seen any such attitudes among the trans activists I’ve been among. AFAIK, it’s taken for granted that gay rights are for the good of society as a whole. We do have feelings of resentment for being treated as an afterthought, as stepchildren of the LGBT movement, in short, we hate being ignored. It’s just too easy to overlook us, to pretend to forget about us. We just don’t have the numbers to be very influential in anything. Gays and lesbians outnumber us by what, something like a thousand to one. Cite: www.gluteo_numeric_extraction.com 
I don’t know what anyone means when they say trans people “are gay” or “are not gay.” Once you enter the trans zone and break down the gender binary, the very definitions of “gay” and “straight” lose their applicability and relevance. I do not think of myself in terms of either category. I don’t define myself by who I’m attracted to. If I were able to totally enter the female identity and be accepted as female, like a successfully passing stealth transsexual, then if I dated only women I suppose you could say I was “lesbian” and if I dated only men then you might be able to get away with saying I was “straight.” But it feels nonsensical to me to think along those lines. I know I’ll always be trans, and as such I’ll always be queer, so don’t you dare call me “straight” regardless of whom I date. Kate Bornstein likes to date women, but she doesn’t claim to be “lesbian” because there is a definite lesbian subculture, or rather a suite of various lesbian subcultures, none of which she really fits into. So she just says, I’m trans, deal with it.
As long as intelligent and caring gentlemen like matt_mcl are around, I believe the gay-trans alliance has a bright future. Thanks for explaining these things so well, matt!