Following the birth in 2018 of two babies from embryos altered using CRISPR-Cas9, human germline gene editing (GGE) moved from abstract concern to reality. He Jiankui, the scientist responsible, has been roundly condemned by most scientific, legal and ethical commentators. However, opinions remain divided on whether GGE could be acceptably used in the future, and how, or if it should be prohibited entirely. The many reviews, summits, positions statements and high-level meetings that have accompanied the emergence of CRISPR technology acknowledge this, calling for greater public engagement to help reach a consensus on how to proceed. These calls are laudable but far from unproblematic. Consensus is not only hugely challenging to reach, but difficult to measure and to know when it might be achieved. Engagement is clearly desirable, but engagement strategies need to avoid the limitations of previous encounters between publics and biotechnology. Here we set CRISPR in the context of the biotechnology and fertility industries to illustrate the lessons to be learned. In particular we demonstrate the importance of avoiding a 'deficit mode' in which resistance is attributed to a lack of public understanding of science, addressing the separation of technical safety criteria from ethical and social matters, and ensuring the scope of the debate includes the political-economic context in which science is conducted and new products and services are brought to market. Through this history, we draw on Mary Douglas' classic anthropological notion of 'matter out of place' to explain why biotechnologies evoke feelings of unease and anxiety, and recommend this as a model for rehabilitating lay apprehension about novel biological technologies as legitimate matters of concern in future engagement exercises about GGE.