This study aims to explore whether children’s food texture preferences are associated with different levels of sensory sensitivity and food neophobia, as well as with other variables, such as parental texture preferences. An online questionnaire was completed by 70 children aged 6–13 years old, alongside one of their parents. Generic texture preferences of children and parents were investigated with the Child Food Texture Preference Questionnaire (CFTPQ). Parents provided background information about their children by completing the Food Neophobia Scale (FNS), the Short Sensory Profile (SSP) and a Food Frequency Questionnaire (FFQ). The results showed that children who differed in their texture-liker status also differed in their levels of food neophobia and sensory information processing: children who preferred softer and non-particulate versions of foods were found to be more neophobic and sensory sensitive across all sensory domains. No relationship was found between parental and children’s texture preferences.