Personalization improves user experience by tailoring interactions relevant to each user’s background and preferences. However, personalization requires information about users that platforms often collect without their awareness or their enthusiastic consent. Here, we study how the transparency of AI inferences on users’ personal data affects their privacy decisions and sentiments when sharing data for personalization. We conducted two experiments where participants (N=877) answered questions about themselves for personalized public arts recommendations. Participants indicated their consent to let the system use their inferred data and explicitly provided data after awareness of inferences. Our results show that participants chose restrictive consent decisions for sensitive and incorrect inferences about them and for their answers that led to such inferences. Our findings expand existing privacy discourse to inferences and inform future directions for shaping existing consent mechanisms in light of increasingly pervasive AI inferences.