I am a Christian because I believe, and because I try to follow the teachings, rightly interpreted, of the Bible.
The fact that the Bible defines homosexual activity as a sin has nothing to do with my belief in the Bible. If the Bible said it was fine, I'd shrug and say "okay then."
I personally prefer not to see two guys snogging in public... but actually I'm not all that big on seeing a het couple trying suck each other's tonsils out in a public place either.
I can't speak for everyone, but in my case it has nothing to do with hate, nor with irrational fear. Personally and politically, I could care less what someone does in the privacy of their home/etc.
However, I'm not going to make myself a hypocrite and claim homosexuality is not a sin according to the Bible when it plainly is. I personally don't go running around grabbing people off the street and telling them homosexuality is a sin... but if someone asks what I think, I'm going to tell them what I actually believe and if they don't like it... well, they asked. Don't ask if you don't want to hear the answer.
The woman in the story engaged the preacher in conversation. If she didn't want to hear it, she shouldn't have asked.
I didn't write the Book, I just try my best to follow it. If you're not intrested in what the Book has to say, don't ask. Walk on.
While we're on the subject of this story, I'm actually not that big on the whole "Street preaching" thing myself. In America, I figure it is covered under the 1A in most circumstances, but personally I think it is a waste of time. It is often condudcted in a confrontational manner, and personally I don't think that confronting strangers on the street is an effective method of witnessing the Gospel.
Assuming we have the whole story, I don't think the preacher should have been arrested, but I wouldn't have been doing what he was doing. Not my sort of thing, not a method I think is particularly worthwhile or effective.