Documents as short as a single sentence may inadvertently reveal sensitive information about their authors, including e.g. their gender or ethnicity. Style transfer is an effective way of transforming texts in order to remove any information that enables author profiling. However, for a number of current state-of-the-art approaches the improved privacy is accompanied by an undesirable drop in the down-stream utility of the transformed data. In this paper, we propose a simple, zero-shot way to effectively lower the risk of author profiling through multilingual back-translation using off-the-shelf translation models. We compare our models with five representative text style transfer models on three datasets across different domains. Results from both an automatic and a human evaluation show that our approach achieves the best overall performance while requiring no training data. We are able to lower the adversarial prediction of gender and race by up to 22% while retaining 95% of the original utility on downstream tasks.