I'm kind of confused about the purpose of this topic. It's like the OP is trying to separate sex/sexuality from emotion. This is almost like asking, "Can you be friends with benefits... with ANYONE?" I don't know if the two can be separated.
Additionally, there have been a few people responding, "I'm attracted to [non-physical features (personality, etc)]." I believe it. But then they're going around the premise of the post entirely. If not attracted to the physical traits of someone, then you must be attracted to something, right? Right?
Otherwise you're just having sex to have sex. In which case, there's something beyond attraction happening there. A need, or perceived need, perhaps? No attraction to the other person? Sex just for the purpose of sex doesn't need attraction. You don't have to be attracted to your right (or left) hand to masturbate, after all.
I'm sexually attracted to women; I'm emotionally attracted to kindness; I'm mentally attracted by intelligence and humor (and puns make my blood flow quite nicely); I'm physically attracted to athletic types - all of the above "categories" go into a qualitative checklist for finding a girlfriend, but other relationships the categories simply don't apply. Friends need not be women nor athletic, but they must have some intelligence and kindness.
Anyhow, back on topic: I think stripping this question down can be an explanatory tool to use to help someone define a basic level of what they want in a sexual partner (or what they don't want), but some people might be tempted to equate sexual/physical characteristics with emotional ones. This can be problematic. I guess I'm just confused as to the purpose of this topic still. Oh well. Hopefully the random thoughts spewed on this page will mean something to someone and the cosmos will go on as intended (or I'll have shifted it enough to make a difference).