I have a friend who has identified as asexual for a long time, and if you were that i think you would probably know it. If not, you have as much right to a relationship as anyone else.
It might be worth looking at the film "Intersexion" by a dear friend, New Zealand filmmaker Mani Bruce Mitchell who recorded the experiences of a group of her Intersex friends around the world. Several of them are or have been in loving long term relationships. It is available on the internet, and well worth looking up.
I myself have pretty much given up actively looking for a relationship with anyone in the cis-lesbian community here, as they can't seem to see past the body parts, in favour of Bi, Trans and Intersex people. Someone who can see past the biology is probably a better bet.
Karen.