I never post anonymously, I personally don't really see the point of it. However, I don't mind when other people use the feature, as long as they aren't using it in order to be hateful to others and hide their username.
I don't post or answer anon. What do I care? Yes it bothers me that others do but Fuck it that's their choice at least they have a choice. Not that matters if you watch the age range and how they type (or come across) you can figure out who they are pretty quick anyway.
I almost never do unless I think that my answers won't be taken seriously because of my age, then "under 18" is better than "14". I don't give anyone a name or a picture though so I'm already somewhat anonymous.