I'm not honestly sure what the definitions of hate, pity, etc are, I can't even say whether I hate them or not. I do know that knowing where the behaviour comes from doesn't make me any less angry.
I usually assume hatred must include wishing ill on someone, in which case I don't hate anybody. But if I wanting someone to stay far, far away from me or wanting to send them to another planet or something is hatred, I'm probably an awful SOB who hates all but the very nicest people.
Pity to me has to include some measure of condescension, so I try very hard not to pity anybody. If I were to do something unequivocally morally wrong, I'd infinitely rather my friends be angry at me than pity me. No one wants to be condescended.
The way you are using the term, though, seems more like what I'd call compassion or empathy, which are good things. And it's probably possible to feel a mix of both compassion and condescension toward someone, I dunno.
I've always defined my attitude towards them as "I pity them, I hate what they say."
Just because I feel some measure of sorry for them because of how much their own fear causes them such anger and hostility, I'm not above getting completely furious at the things they say.
Though I have gotten better at dealing with their nonsense rationally as the years went on. You compare me arguing with a homophobe now to me arguing with a homophobe a couple of years ago and you'd think it was two entirely different people. I was so much more aggressive and dickish back then. Not that they didn't deserve some of it, but I realised that I wasn't helping my case when I tried to talk sense into, for example, an anti-gay marriage person and there I was ranting like an angry lunatic about how stupid and pathetic they were.
Better to talk about it sensibly than to just start yelling. Though I do admit that some specific types of homophobes still instinctively inspire nothing but pure rage and vitriol in me.
For example: Comparing homosexaulity to stuff like pedophilia, bestiality, necrophilia or anything like that? That's a guaranteed one-way ticket to seeing me at my most angry.
Whereas comparing it to polygamy is a ticket to seeing me at my most amused because it's such a failed argument when used against someone who sees no problem with polygamy being legal.
Also just want to add on a slight tangent since it was mentioned earlier: When it comes to my place in the whole 'gay rights' thing, I always feel like I'm useless. My contribution to the advancement of LGBT equality is limited to arguing with idiots over the internet. I always feel like I should be trying to get more involved, somehow.
Just don't really know how.
I don't the "it's a choice" thing, either. I wish our sexuality and sexual nature WAS a choice; wouldn't that be wonderful? There are things about my sexual nature that I would definitely be working on if there was actual choice involved. But there is no choice.
I would say I wish there was a choice involved, but I know that if there was then at my weaker, more pathetic moments I would willingly give up being gay. And while I feel like sometimes being gay has kind of doomed me to a life of loneliness and sadness, and like it'd just be so much easier to be straight, I still would never be able to live with myself if I opted to change that part of myself.