Right-wing populists have recurrently created moral panics internationally about the supposed need to 'protect free speech' in higher education (HE), and 'protect children' from progressive speech in schools. This paper presents the first systematic analysis of how such dynamics function with respect to race and faith equality in a national school policy context. Drawing on a critical post-structural framework, we conceptualise the policy problematisation of "speech" as situated in a wider set of coercion-consent governing strategies used to manage contemporary authoritarian neoliberal contradictions, and to narrow the "speakability" of anti-racist and faith equality concerns. We present a two-stage thematic and discursive analysis of a corpus of primarily school-focused English policy texts from successive Conservative-led governments (2010-2022). The analysis outlines three main policy strategies which narrow speakability: the defining of 'good' schools and citizens with limited/oppositional reference to race equality, the problematising of 'dangerous' speech, and the indexing of school/HE subjects who are "truly" vulnerable to political speech. The paper offers an urgent case study of how possibilities for progressive race and faith-based expression are shaped beyond explicitly speech-focused policies, and argues that engagement of the complex governance of speakability offers nuanced possibilities for analysing bans on progressive education internationally.