Cultural code-switching concerns how we adjust our overall behaviours, manners of speaking, and appearance in response to a perceived change in our social environment. We defend the need to investigate cultural code-switching capacities in artificial intelligence systems. We explore a series of ethical and epistemic issues that arise when bringing cultural code-switching to bear on artificial intelligence. Building upon Dotson's (2014) analysis of testimonial smothering, we discuss how emerging technologies in AI can give rise to epistemic oppression, and specifically, a form of self-silencing that we call 'cultural smothering'. By leaving the socio-dynamic features of cultural code-switching unaddressed, AI systems risk negatively impacting already-marginalised social groups by widening opportunity gaps and further entrenching social inequalities.