Shopping 613, a real Jew has a Jewish mother or a halachic conversion. Period.
Beyond that, you get in to “my kind of Jewish practice is better, or more complete, or more ehrlich, or more strict, or more valued by HKBH” (which might carry some accuracy from a personal perspective) and therefore I am a real Jew and you are less so (which is simply false).
And that’s just between ostensibly frum or chariedi groups.
I don’t understand the need for measurement of any element of one’s Jewish life versus another Jew. Measure yourself against the goals and standards Hashem sets for you and that you take on the responsibility for. That is really the only measurement that matters. And the only judge is the one in shomayim. He knows who is a real Jew.