IRL, are you a politician? Let me clarify for you. I am fully aware that just because someone calls themselves a Christian doesn't always mean they're Christians. I'm in the Presbyterian Church of America (PCA.) My denomination is made up of mostly people who are Christians, but in that group I'm equally as sure not all of us are. Just the same, if someone to ask, "Are PCA's Christian?" I'd answer Yes.
This is that kind of question. It's not searching down into the soul of each individual. It's looking at a group and then deciding, for ourselves, if that particular group is out to follow Christ, not if everyone in that group is.
AND there are labels, and those labels are a good thing so we can figure out the basic message behind a group to determine just this kind of thing in a generalized why. So, of course labels don't save, but they do tell something about the thing being labeled. You know this because you're out to be labeled in the group that believes "saved by grace."
So, once again, want to try for clarity?