ROB: I’d rather not get into an extended discussion, since your earlier posts appear too nonsensical for me to even try understand, and that’s without requesting you punctuate your posts in manner that might make them at least partially legible. But I’ll happily respond to this one point, despite having already made this distinction several times extremely clearly.
A person committing an aveiro is not therefore irreligious. People slip from time to time. However, if a person is acting based on an ideology, and wilfully sinning as a result of this ideology, in an extreme example, somebody who is living and continues to live in a relationship with a goy (if that ‘extreme’ example is suitable to you), then certainly that person cannot be considered a practising Jew, even if they still keep many other mitzvos perfectly. Because they aren’t just sinning, they are rejecting the Torah ideologically and practically, and there is a world of difference between the two.
The State, too, by, for example, actively tolerating and promoting toeiva, is guilty of not just erring, but of actively rejecting Hashem and His laws. A few token motions do not negate this. And I’ve already made this clear.