The following contains mild spoilers about “Zero Day.”

Conspiracy thrillers can feel like a dime a dozen in this age of streaming and limited series, with everyone looking for a good binge, filled with suspense and mystery, to take them away from it all, if only for six or eight hours.

Yet amid the chaotic, unsettling nature of the current political moment, such material hits differently, and especially so with Netflix’s latest entry in the genre, “Zero Day,” which consciously leans into current events — down to its slogan, “The Truth Has Been Weaponized” — by conspicuously and self-consciously paralleling them.

In that sense, the six-episode project that premiered Friday potentially lays bare a challenge facing development executives more broadly as they look ahead, to the extent the show’s themes come across as less escapist than exhausting.

Marking his first foray into TV series, Robert De Niro heads a genuinely star-studded cast,...