Suppose your categories were indeed listed, and somebody would write something unclear, then some people might say to themselves: "Well, this person belongs to category X, so they must have written something that's in line with X. Although I don't quite understand what they wrote, I won't bother to check by asking what they meant." You wouldn't want that to happen, would you? Because it would mean that discussions would be over before they even got underway.
I'm not so sure it would work like this. If somebody posted something unclear, and I knew that that somebody were, say, a theistic evolutionist, then knowing that might help me to understand just what he was saying. And knowing his position doesn't really stop me from asking for a clarification; I think people ask for clarifications from well-known evolutionists/creationists all the time in this forum.
I don't "belong" to a position, it's the other way around: my position belongs to me.
Well yes, you're right, but this is just semantics. Consider my proposal to be restated as something like "members could somehow identify which position(s) belong to them..."
Besides, my position might change. What you propose suggests too much rigidity for my taste.
This would be an issue, yes, but not an insurmountable one. The change could be designed to be flexible; people could sign up to have many positions, or one labeled "undecided," or not sign up for one at all. It will just have be be a balance between flexibility and usefulness.