I always wondered why do people that practice Buddhist practices, label or opt not to label themselves "Buddhist".
All labels are conventions & attachment to mental states of non-becoming can make the mind uncomfortable with conventions.
Also, the term 'Buddhist' is a stereotype, loaded with all kinds of worldly connotations, such as believing in the Dalai Lama, reincarnation, statues, etc.
Those people might be more comfortable if asked: "Do you practise the teachings (path) of the Buddha?".