Hi Suzumi,
I've found the three divisions of the noble eightfold path a very useful framework to apply to complex things like self-identification. As I indicated in my previous post, the way I use this is to separate out the "everyday life" and "ultimate wisdom" bits of the issue, so they can be worked on in the context appropriate to them.
So, in my experience, whenever I start to treat social interaction as a stream of meaningless babble pillowing my attention, I run into trouble - because that's not a helpful way of dealing with it, neither for me nor for the people I interact with. Instead, going for kindness and compassion (and really going for it; sometimes less is more when it comes to engaging compassionately, depending on all kinds of circumstances) is key when moving in society. By this I don't mean to say, "I'm Buddhist, look at how kind and compassionate I am", but instead, working really hard on all the babble, content and "stuff" I contribute to all the babble already out there. Going for "quality babble" (and other high-quality behavior) over just any old mindless babble

This I understand to be what the "morality" or "sila" or "virtue" part of the noble eightfold path is all about. While eminently mundane, this IS a full 1/3 of "heading toward the goal".
On the other hand, on the ultimate wisdom, insight partition of the eightfold path, I leave the tiresome content of the babble aside, and instead train myself to see it just as babble (even the quality babble): transient, not ever permanently satisfying, causal, not something I can identify with. This is where even identifying as Buddhist (or deliberately not identifying as Buddhist) is just another bit of babble that will have its say and then subside. Here, it's key to be able to see suffering, impermanence, and not-self.
(cont.)