Conservation management is a rapidly evolving field in which scientific innovation and management practice can run ahead of social acceptability, leading to dispute and policy constraints. Here we use best-worst scaling (BWS) to explore the social preferences for two broad areas of threatened species management in Australia as well as support for extinction prevention as a whole. Of the 2430 respondents to an online survey among the Australian general public, 70% stated that extinction should be prevented regardless of the cost, a sentiment not fully reflected in existing policy and legislation. There was strong support for existing measures being taken to protect threatened species from feral animals, including explicit support for the killing of feral animals, but the demographic correlations with the results suggest approval is lower among women and younger respondents. There was a particularly high level of support for moving species to new places, which does not match current capabilities of managers responsible for assisted migration, suggesting messaging about the current limitations needs to be improved, or for resources to overcome them greatly increased. There was less support for genetic interventions than the feral animal control and other land management measures. A small majority of respondents thought it would be better for a species to cope without assistance than invasively alter their genome. This suggests that greater community consultation is desirable before applying genetic management approaches more interventionist than interbreeding subspecies.