Omnisexual
Omnisexual often can be interchanged with the term Pansexual, though there are those who will argue the two are different. Omnisexuals are people who feel attraction towards people of any gender and orientation, including male, female, genderqueer, transvestites, bisexuals, straight, gay, lesbian, asexual, and so on. Omnisexuals see people for their personalities rather than their genitals or gender identity. Omnisexual is not a cover term used for people who will date transsexuals. Bisexual, Gay, Straight, and Lesbian SHOULD cover these terms. A well known phrase of the Omnisexual/Pansexual community is "Hearts Not Parts".
A famous example of an Omnisexual is Captain Jack Harkness from Doctor Who or Torchwood. If it has a pulse, he'll flirt with it. If it doesn't... He'll probably do it anyways.