Demistraight
Demistraights are attracted to the opposite sex physically, but refuse to be in romantic or sexual relationship to any person unless they become deeply emotionally or romantically connected with that specific person. The level of connection it takes for sexual desire to form is dependent on how close the relationship is rather than initial attraction.
Im not Exactly a Demisexual because I am still only attracted to men, but only on a deep emotional level, so I'm a Demistraight