As chatbots become increasingly widespread, personalization has emerged as a key feature for accommodating diverse users and use cases. Personalization enables better responses rather than generic answers, but when using demographic attributes to drive recommendations, can also amplify harmful stereotypes. For instance, individuals from different cultural backgrounds may meaningfully want culturally distinct food preferences and values incorporated, but not different job recommendations. Yet, little is known about how these user preferences relate to actual platform behavior. Through a survey of user preferences and a novel field study methodology where users input our standardized questions to their own personalized chatbot interfaces then share the outputs back to us, we contribute real-world personalization insights on the gaps between what users want versus actually receive. We generally find that there is minimal race- and gender-based personalization in practice, which conflicts with users’ desires in some domains, e.g., cuisines. We conceptualize our findings through the framing of a personalization double bind: Black people and women desire more demographic-based personalization than White people and men in order to avoid overly generic responses (indirect discrimination), yet simultaneously express greater concern about stereotypical responses (direct discrimination).