Which word would describe someone who is careful not to disclose sensitive information?

The word that best describes someone who is careful not to disclose sensitive information is "discreet." Discretion involves maintaining confidentiality and exercising prudence in speech and action, especially when it comes to handling sensitive or private matters. A discreet person understands the importance of safeguarding information and can navigate conversations and situations in a manner that protects that information from being shared inappropriately.

In contrast, the other terms do not align with the concept of carefulness in protecting sensitive information. Disrespectful implies a lack of regard for others, disruptive suggests causing disorder or interruption, and disinterested refers to being impartial or lacking interest in a particular matter. None of these convey the carefulness associated with being discreet.