This article tackles one of the latest—but nonetheless baffling—displays of public apathy towards surveillance: that of much of the Israeli public towards the decision to recruit the Israeli Security Agency (Shin Bet) to do COVID-19 contact tracing during the ongoing coronavirus pandemic. The case of a secretive state agency being authorized to do surveillance on its citizens for a strictly non-security-related matter seems to realize many of the dangers that surveillance/privacy scholars warn about with regards to surveillance expansion, function creep, and the creation of a surveillance state. I contribute to existing literature about apathy towards surveillance and the privacy paradox by offering the term “nontargets” as an explanation. This term suggests that, alongside social groups that are likely to be targeted by a given surveillance application, there are certain recognizable nontargets that most likely will not bear the brunt of the surveillance, at least not in the short- and medium-term, and thus do not fear it. In the case at hand, which is examined using a qualitative context-bound study, I suggest that Jewish-Israelis are such a nontarget group with regards to this novel Shin Bet surveillance, which explains a significant part of their apathy towards it.