You’re correct. The term “Jewish” is complicated by the fact that it traditionally referred to both a nationality and a religion. The two were synonymous for most of their history. Judaism developed at a time when religion was tied to nationality more strongly than it is today. Judaism originally meant simply, the religion of the Jews. As religion has come more separated from nationality in modern times, you have the odd situation that a good portion of people who identify as Jewish no longer follow Judaism. Complicated.
Jews have been disobeying God since the Golden Calf.