Is it possible to avoid those types of conversations? (that's what I would do. out of sight (ears), out of mind) or are other people starting the fights with you. If so don't participate, walk away, tell them you don't want to discuss it because it's not going to accomplish anything good. Don't go around reading blogs that you know will upset you. If it's just the thought that there are people out there who share those opinions, I guess it's a little harder to get over.
Personally, I try not to demonize people (though I often can't help myself). In this case, I'm sure you can understand where these people are coming from. Even if it's not right, and even if their rejection of androgyny is selfish or whatever you want to call it, they're only people, and we can't expect them to completely understand things that they are unfamiliar with, or to accept things that for one reason or another they believe are hurting them/increasing the likelihood that others will reject them. Maybe they're drawing conclusions from information that isn't right, or from a couple examples that don't represent the group that they are associated with, or maybe neither is the case.
It's not fair, and I wish that people were more altruistic, but they are what they are, and I have trouble blaming them for it. Plus, people have a natural tendency to separate things based on differences, because it helps them get a grip on what things are and what they mean. and when you are so used to gender separating, boy toys, girl toys, boy clothes, girls clothes, and so on with colors bathrooms etc etc, the concept of a person who identifies as neither gender is sort of abstract. It's not gonna be easy for everyone to understand. I know it's impossible to be impartial, but try as hard as you can to understand why they feel/behave the way they do. If you shared all their experiences, and weren't androgynous, do you think you would be that much better than them. maybe maybe not.
I know the whole "walk in their shoes" thing is cliché, but if you really give it a chance, it might be comforting. It doesn't make them right, and it doesn't mean that we shouldn't work to change the way people feel, and to help them feel comfortable with things they aren't familiar with, but sometimes to keep your sanity you have to find a way to ignore hatred, and to not hate them back.