High dynamic range (HDR) imaging has been developed for improved visual representation by capturing a wide range of luminance values. Owing to its properties, HDR content might lead to a larger privacy intrusion, requiring new methods for privacy protection. Previously, false colours were proved to be effective for assuring privacy protection for low dynamic range (LDR) images. In this work, the reliability of false colours when used for privacy protection of HDR images represented by tone-mapping operators (TMOs) is studied. Two different TMO techniques are tested, a simple TMO based on the Gamma transform and a more complex local TMO. Moreover, two false colour palettes are also tested, and are applied to images that result from both TMOs and also to an LDR image that represents the centre exposure in the image sequence used to create the HDR image. The degree of privacy protection is analysed through both a subjective test using crowdsourcing and an objective test using face recognition algorithms. It is concluded that the application of the two studied false colour palettes reduces the recognition accuracy with respect to both tests.