We use the term re-identification to refer to the process of recovering the original speaker's identity from anonymized speech outputs. Speaker de-identification systems aim to reduce the risk of re-identification, but most evaluations focus only on individual-level measures and overlook broader risks from soft biometric leakage. We introduce the Soft Biometric Leakage Score (SBLS), a unified method that quantifies resistance to zero-shot inference attacks on non-unique traits such as channel type, age range, dialect, sex of the speaker, or speaking style. SBLS integrates three elements: direct attribute inference using pre-trained classifiers, linkage detection via mutual information analysis, and subgroup robustness across intersecting attributes. Applying SBLS with publicly available classifiers, we show that all five evaluated de-identification systems exhibit significant vulnerabilities. Our results indicate that adversaries using only pre-trained models - without access to original speech or system details - can still reliably recover soft biometric information from anonymized output, exposing fundamental weaknesses that standard distributional metrics fail to capture.