One is not Jewish by birth anymore than one is Catholic by birth ( no matter what your folks may have taught you). Ethnicity is about your blood lines ( eg Caucasian, Negroid, Asian, Semitic,etc). You don’t get to redefine things just because there are cultural ‘jews’
Okay, but I will go with the word of my wife’s rabbi who understands that there are ethnic Jews and those who practice Judaism. Simply, a person may reject their faith but they cannot reject their ethnicity.
1. one of a scattered group of people that traces its descent from the Biblical Hebrews or from postexilic adherents of Judaism; Israelite.
2. a person whose religion is Judaism.
3. a subject of the ancient kingdom of Judah.
You seem to be stuck on the secondary definition. The primary definition is the most common and requires no religious affiliation.