JCPA is a very realistic, sober and exact organization.
Almost universally in America, for census and polling purposes, a ‘Jew’ is someone who self-identifies as such.
By contrast, lists of ‘Jewish’ celebrities don’t really have consistent standards at all. People are just deemed Jewish whether they are or not, or whether they want to be or not.
An example of JCPA best work:
I've read that the Reform definition of a Jew is anyone who...
1. Has any Jewish heritage on either side of the family, and
2. Identifies as Jewish.
So if you have a paternal great-grandfather who was Jewish and you identify as Jewish, then you're Jewish.