Daniel will soon be meeting with a person who, well, didn't like him being at BYU or speaking up as an out gay man. He wrote a great response and now she has reconsidered and is looking to meet face-to-face.
I've spent maybe too much time searching out such folks and well know that feeling of walking into a room where you're sure you'll face some of the most horrible ideas about you and yours. I'd not say I'm any good at it, but I still do it because the fate of my family depends on resolving this conflict. I can say though I have, more often than not, been very happy I got past the discomfort and just did it.
So, for what it's worth, what I have learned:
I'd not look at face-to-face meetings with opponents as a debate. It's absolutely different if you have an audience and you're both on a panel or something. In that case you'll need to get right to it and have organized data and research at the ready. In the time you have, your opponent is a lost cause and it's your audience with the open minds. You'll have to be defensive and watch out for tactics like having your positions defined before you get a chance. I know because I, long ago, was on a panel thinking of it like it was a person-to-person meeting and I got pwned by Gayle Ruzicka :-). Won't let that happen again.
However, I'd see first person-to-person meetings under such circumstances as a time to develop the rapport that will be needed to discuss such topics productively in the future. It's pretty clear why this issue is stressing for gays, and it's clear there's a great asymmetry in potency: no anti-gay rights activist has resorted to suicide because the gays get the same rights they have. Some of that difference and insensitivity to it may need to be swallowed at first and some punches may need be adsorbed.
So, I'd first look to hear her out. While our fears are clear, the other side seems to have many different triggers, each with different answers. I'd try to figure out why exactly this holds so much "emotion and frustration" for her, and even if the reasons are demonstrably baseless, I'd let a lot slide for a later meeting. Still, I do take all the information I'd need in a debate, but would leave it in my backpack or car until she seemed to be asking you for facts about a fear expressed or question asked.
In short, I think Daniel's instinct to stay away from politics for now is a good one. Once a foundation is set, then I'd go on to pleading my case in later interactions.
A couple other things:
It's natural to feel that fight or flight reflex when you know you're approaching a confrontation. I get butterflies every first meeting with anti-gay activists. However, this person in question didn't come off as a seasoned stone-hearted anti-gay activist in her letters; more like someone caught up in the Prop 8 fight? I'd keep in mind, if you get nervous, that she may be more afraid of you, thinking of you as some big Act Up in-your-face hostile queer; that always calms me down. Just don't picture them nude; that's exactly what they'd expect :-).
Also, I don't care to remember how many times I've felt a friendship build with such opponents, feel, by their words, we've come to an understanding and mutual respect, and then find they turn on me and my family and their kind words change when they think they're just talking to their side. It's tough for me to not become invested; I feel myself doing it again with the Evangelicals I've been meeting with. I'm just saying, I'd be friendly, and open, but remember some humans were even able to "love" the gays they were torturing to death to gain what they thought was a heaven-granting confession, and we're just talking about stuff like taxes and health insurance here.I'd not put too much of myself into such relationships, anymore.
Lastly, meet in public, of course. There are crazies out there. Don't meet on BYU's campus either. I hear there's a gay reeducation dungeon buried deep below the Cougar Eat, and you don't want to make it easy to be dragged anywhere ;-).