I think it's important to remember that when you are interacting online, especially with an unknown person, there is no relational component. You are effectively just words or text to them, there isn't a "person" behind what they are reading. It's very easy to be obstinate or argumentative with just words because you can't see the reaction or impact on the other person. So it's nearly impossible to change someone's mind in that format unless they are really being genuine and looking to have an exchange of ideas.

I've found the best way for myself to handle these types of situations is to realize nothing I say is going to impact them or change their mind. If I'm really wound up I might type a response out to get the frustration and energy out and then delete it. I usually feel better after that and can move on with my day but engaging further is just going to lead to further frustration because you can't actually reach the person.