it is different. Don't they still think of themselves as Hoklo or Hakka? If so, then they cannot deny that they are Chinese, since Hoklo & Hakka are Chinese.
You're still making a decision for them when you write that, and some people may still not want to be included in any variation of Chineseness, and still have their own reasons for doing it. I don't know any people like that myself, but I'm sure they do exist, and that they do have their reasons for existing. In any case, I'm sure most of the Taiwanese who say they aren't Chinese are merely saying that they are not Tiong-kok-lâng and not denying their Tng-lâng-ness or 華人-ness and that the issue is more of English confusing membership of political and other entities.
There are plenty of people whose ancestors came from what is now China in western countries who want nothing to do with it. I don't see any problem with it. One's culture and interests need not always be determined by our genetic ancestry I think. One day the balance of power might be different and the descendants of English people might not care about learning English. I wouldn't blame them for that either.
As a digression, one of the interesting things I learnt last year was that the Ch'ing government did not consider Chinese who had converted to Christianity as Chinese any more, so they were permitted to stay in Macau overnight, when the other Chinese were not.
It's interesting that though similar, "ethnicity beliefs" and religious beliefs usually move toward opposite directions, i.e. in claiming separatist identity for the former and established identity for the latter (e.g. Mormons/JWs claim to be Christians while most Christians view them as heretics; Yiguandao in Indonesia claim to be Buddhists, etc).
As far as I know I-kuan-tao will sneakily pretend to be just about anything (Taoist, Confucianist, Catholic) to get converts. I had a run in with them in the late 1990's when they were trying to rope people in through language exchanges and nice vegetarian food. I found out what they were called from someone else, and when I asked them "what is your religion called they said "It doesn't have a name , it's just the truth." If they had said "Well, some people call us I-kuan-tao but we think...." then I would have accepted it, but since they chose to lie about it, I decided their moral teachings were a bit weak and it probably wasn't worth having anything to do with them any more. Plus they used to get all fussy about eating sour cream and chives potato chips, try to indoctrinate me in the evils of garlic, and you should have seen the look on the man's face (he usually had a sort of dreamy, smiley look) when he saw that I had brought back from Taiwan one of those electrified badminton racket-type things that kill mosquitoes! I also happened to notice from a schedule hanging on the wall what time they got up in the morning and how many hours a day they spent praying. I decided to make a break for it then!
(just edited this to apologise for the blunt tone, I think it was the shortness of the sentences that does it. I've been on night shift and had no sleep, and I can see how it has affected my writing by making me unable to string long complex sentences together!)
