Is religion, or in our case historical Traditional Judaism, relevant? Yes, of course it is. Historical Traditional Judaism is relevant because, given the concerns that people typically have, the Torah has a very good track record of producing results.It is fortunate that Rabbi Dovid Gottlieb limited his list of crimes to violent ones. That way he doesn't have to worry about removing money-laundering, tax evasion, organ trafficking, child labor violations, identity theft, bank fraud, immigration violations, etc., from the next edition of his booklet "Living Up To The Truth" (although he probably should delete child abuse from the list of "almost unknown" crimes.)
Everyone wants to live with as little crime as possible. Again, Jewish Tradition is very proud that within Torah communities, crime, violent crime in particular, is almost unknown. Imagine interviewing the presiding police officer in a precinct in Williamsburg, Borough Park, Flatbush, Monsey, Monroe, or any place where you have large concentrations of Traditional Jews. Ask him how many times he is called out on a murder charge, rape, assault and battery, mugging, child abuse, etc. The incidence of these sort of crimes in Orthodox communities is very low.
(As readers of my sporadic blog may know, Gottlieb's writings generally rank very high on the bogometer, as described more fully in God is a Mafia Boss. But if you are ready for some more Gottlieb-style logic that allows him to conclude his thesis with "Therefore, Judaism is the only justified way to live.", you may view the booklet in its entirety here.)