Cybernetic avatars are hybrid interaction robots or digital representations that combine autonomous capabilities with teleoperated control. This study investigates the acceptance of cybernetic avatars in the highly multicultural society of Dubai, with particular emphasis on robotic avatars for customer service. Specifically, we explore how acceptance varies as a function of robot appearance (e.g., android, robotic-looking, cartoonish), deployment settings (e.g., shopping malls, hotels, hospitals), and functional tasks (e.g., providing information, patrolling). To this end, we conducted a large-scale survey with over 1,000 participants. Overall, cybernetic avatars received a high level of acceptance, with physical robot avatars receiving higher acceptance than digital avatars. In terms of appearance, robot avatars with a highly anthropomorphic robotic appearance were the most accepted, followed by cartoonish designs and androids. Animal-like appearances received the lowest level of acceptance. Among the tasks, providing information and guidance was rated as the most valued. Shopping malls, airports, public transport stations, and museums were the settings with the highest acceptance, whereas healthcare-related spaces received lower levels of support. An analysis by community cluster revealed among others that Emirati respondents showed significantly greater acceptance of android appearances compared to the overall sample, while participants from the 'Other Asia' cluster were significantly more accepting of cartoonish appearances. Our study underscores the importance of incorporating citizen feedback into the design and deployment of cybernetic avatars from the early stages to enhance acceptance of this technology in society.