Who is a Jew?

In fact, is someone who does not observe Torah and commandments not a Jew?

clear.

So why is it forbidden to convict him of a crime if he is not Jewish?

Or to be more precise, why does the global consideration of preventing a Jew from committing a crime also apply to him?

First of all, who said it was forbidden?
Second, it is forbidden to offend a Gentile as well.
And third, I was talking about his Judaism, not his Jewishness. Judaism is halakha. A Jew is anyone who was born to a Jewish mother or converted.
It is clear that he is obligated to the commandments even if he does not understand it.

Certainly, Haredim who disdainfully disregard the commandment of Ezrat Yisrael from a narrow path are not Jews.
In fact, there are only three Jews left in the entire world

To which law exactly should one be committed? No two Jews are exactly the same
Are Yemenites considered Jews even though they are committed to different laws? Is a Muslim who is committed to Shia considered a Jew?

Nehemiah the Amasoni,
Are you asking seriously?