The degree of accuracy of the three statements you mention might be calculated by accurately determining what percentage of Jews, Gypsies and Italians actually are “notorious thieves, and Societal nuisances.”
Certainly any such statement is never true of all members of a group, but as the percentage for which it is accurate increases, it becomes progressively more true as a general statement.
Your comment reminds me somewhat of the liberal shock when waitstaff (including black waitstaff) are resistant to serving black groups because of the “stereotype” that blacks are cheap tippers. No research project could be simpler than determining whether blacks (as a group) do indeed tend to stiff waiters, but somehow liberals are utterly uninterested in doing this basic research.
IOW, some stereotypes are quite accurate in the generality, although often unfair to particular members of a given group.
“...waitstaff (including black waitstaff) are resistant to serving black groups because of the stereotype that blacks are cheap tippers...”
Everybody knows its true, knows there are exceptions, but it is to the point where waiters and waitresses will leave certain establishments if they become too Black. It is not based upon prejudice. It is based upon personal day to day experience.
Gypsies as a group are right down there with pirates in reputation and for good reason.