You can view it like a public bulletin board; everyone is posting to the public even if it is about a different sign, that could have been written by someone from the other side of the Mechitza.
There are, however, two other issues. There must be a level of appropriateness. Although you don’t know the other person, so there is no real Hirhur involved, it is still inappropriate. It is a style and behavior issue. The other point is that there is a level of Al Tarbe. Chatting over the Mechitza is a whole different conversation, and anyone keen enough can spot it.
As many have said, when boys and girls are talking it is a whole different thing going on. Many studies have shown how the behavior of each one changes in the presence of the other. If you follow the threads that turned trans-Mechitzadic and personal, you’ll notice how it spirals into a game and being cute and some me-and-you talk. That is still not technically Hirhur, but it falls into some other categories.
Because of this approach, I do respond to posts written by anyone, because I’m writing to everyone. (The person him/herself usually doesn’t end up agreeing anyhow, so what would be the point of writing if it were only for that poster?) However, I’d refrain from kidding around and even addressing someone that has an obvious other-gender screen name. I just can’t find myself saying, “Hey, Sister…”. Address the point, not the person.