One reason to classify beliefs as contrarian is that it helps you discuss them more effectively. My presentation of an idea that I expect will seem contrarian is going to look very different from my presentation of an idea that I expect will seem mainstream, and it's useful to know what will and won't be surprising or jarring to people.

This seems most relevant to stage 3-- if you hold what you believe to be a correct contrarian view (as opposed to a correct mainstream view), this has important ramifications as to how to proceed in conversation. Thus, knowing which of your views are contrarian has instrumental value.