I'd amend it to "Judaism is whatever people who claim to be Jewish do that they say is part of their religion."

(nods) OK, understood. I'm not sure that's a particularly informative place to carve, but it's at least coherent.

I admit I want some consensus exceptions for Jews for Jesus (from what I'm told, actually Baptists) and Christian Identity (white supremacists who claim to be the only Jews).

I understand why, though I wonder how viable that is. I mean, sure, it's probably true that approximately all non-JfJ soi-disant Jews agree that the JfJ are no more Jews than the Jehovah's Witnesses are. Then again, it's also probably true that approximately all haredim would agree to something similar about Reform Jews. And as long as we're ignoring some people's self-labeling, I'd sort of like to put in for an exception excluding the haredim, come to that; I'm a Jew, but I don't do what they do.

Which I guess is OK, it just leads to lots of different mutually exclusive things to which the label "Judaism" applies, and the need to resolve what Judaism we're talking about before the conversation gets too far. Which happens a lot with language anyway.