Now, I have no idea at all about role-playing, but to me it seems that the logical way to go about playing a character who does not want to get into a homosexual relationship would be to just react to any homosexual advances by having the character state that sorry, but they aren't interested.

Rule of thumb; people's characters will generally have less breadth of imagination than the people who play them. And some people can't possibly imagine that a G/L/B person of the same sex might come within 100 yards of them without experiencing the uncontrollable compulsion to have sex with them by any means necessary. So it seems that for certain RPers, the imagination constricts to the point where "100 yards" becomes "the same plane of existence".