When people talk (in English) about being 'Chinese', the discussion is muddled by the fact that 'Chinese' in English has multiple senses.
Critics of multiculturalism sometimes counter that there is no way a foreigner can become 'Chinese' - but really, this depends on what you mean by being 'Chinese'.
Mandarin is more helpful in delineating the different senses of being 'Chinese' (as one might use the English term):
中国人 - Chinese (nationality)
华人 - Chinese (ethnicity) - including the 55 officially recognised ethnic minorities (at least from the 20th century onwards)
汉人 - Someone of Han Ethnicity (about 92% of China's population)
华侨/华裔 - Chinese (diaspora)