The ability of modern telecommunication systems to locate users and objects in the radio environment raises justified privacy concerns. To prevent unauthorized localization, single-antenna transmitters can obfuscate the signal by convolving it with a randomized sequence prior to transmission, which alters the channel state information (CSI) estimated at the receiver. However, this strategy is only effective against CSI-based localization systems deploying single-antenna receivers. Inspired by the concept of blind multichannel identification, we propose a simple CSI recovery method for multi-antenna receivers to extract channel features that ensure reliable user localization regardless of the transmitted signal. We comparatively evaluate the impact of signal obfuscation and the proposed recovery method on the localization performance of CSI fingerprinting, channel charting, and classical triangulation using real-world channel measurements. This work aims to demonstrate the necessity for further efforts to protect the location privacy of users from adversarial radio-based localization systems.