It's perfectly acceptable to be secular and still consider yourself to be Jewish.
If you're "Christianed" or "Baptised" CofE and Catholics will both mostly consider you Christian even if you're an atheist by confession.
The issue is that religious actions become cultural actions. And that religious leaders claim people as their own.
People who live in Thisistan are Chrewslims; or people whose parents were Chrewslims are also that. Silly.
It is weird how culture and religion become decoupled and religious actions become cultural markers.