I don't have an issue with sexualities except the transgender sexuality. For me it's the only one that seems to inherently pose sociological issues.
For me, and this may be ignorant, if you're born a man you're a man. I completely understand that you identify as a woman, and respect that, but you have to understand that you're genetically male. If you pursue a relationship, which you may view as an opposite sex relationship, you're truly pursuing a same sex relationship.
Ultimately in this scenario it is up to the transgender individual to be forthcoming with their partners, but I'd imagine a lot of transgender persons would hide the fact that they're transgender since they believe they're the sex that they present themselves as, or fear rejection. I'd imagine, perhaps ignorantly so, that a large majority of heterosexual individuals would not engage in a relationship with a transgender person if they knew their sexuality beforehand. And if their longtime partner came out as transgender down the road, they may indeed terminate the relationship, this could be attributed to the trust issues that would go with something like this, aside from the physical issues.
Again, as a very particular example, if you are born a male but identify as a female, I don't think you should be allowed to compete in female sports. Just because you identify as a female, that does not mean you can play in a female hockey league. You are genetically a man, you have bigger bones, bigger muscles, lower percentage of fat, and generally larger frames. Currently there is an issue in the MMA world where a transgender person that identifies as a female, though born a male, and she wants to compete in the female fighting division. Which, in my opinion, is completely absurd.
Regarding persons whom are gay or lesbian, I don't give a **** that you're homosexual, just like I don't care if someone is heterosexual. Do whatever you want, love who ever you want, doesn't make a lick of difference to me. They should be allowed to participate in anything a heterosexual person can.