With Big Tech’s growing encroachment into all aspects of human life, it is no wonder that museal institutions are, too, becoming enmeshed with them. In this article, Brian Castriota and Hélia Marçal analyse the emerging technological ecologies infiltrating museum management and conservation. They offer a critique of the museum sector’s dependency and complicity with forms of platform capitalism via their entanglement with cloud-based digital preservation and management systems. They argue for refusal as the ultimate act of affirmation and care.