Absolutely. In general, if there’s a sexual component to their killings, their victims will be the sort of people that they find attractive. A straight man who hunts other straight men would be very unusual, although not unheard of.
Regarding the difficult, you should write that into the story. Have the killer go into a cross dressing bar or drag queen hang out to work up the gumption to killing a woman. Just a thot.
Or just make mention of the killer’s feelings on the same point. Perhaps describe a moment where the opportunity arose, and he couldn’t go through with it. Use your own feelings of disgust to flesh out his character. There’s no reason why a killer couldn’t have his own ethical limits; in fact, that’s probably more realistic.