✔ 最佳答案
First of all, I would like to point out that, there is no such thing as Hong Kong Citizenship and Taiwanese Citizenship, only Chinese Citizenship (PRC Citizenship or ROC Citizenship) But Chinese Citizenship will do in this case.
You do not need to give up your ROC Passport, because it is simply not recognised in HK. HK will simply considered you as a Chinese Citizen WITH Taiwan PR.
The answer is YES. You may apply a HKSAR Passport after you have a HK Permanent Residence ID (normally after 7 years of residence in HK) without giving up your Taiwan Passport and ID.
But the problem is you POSSIBLY cannot use HKSAR Passport to enter Taiwan, becaue the "Place of Birth" column on the Passport would have betrayed you as a (ex-)Taiwanese. Taiwan authority only expect HKSAR Passport holder to be born in HK and Mainland, not Taiwan. So I m sure they will be suspicious about your origins and may conduct an identity check on you. Your military obligation would have shown up by that time.
If you want to avoid this responsibility, you must make sure you will never need to go back to Taiwan ever again or use fake passport or false identity (kidding). Unless you do not have much connections in Taiwan (family, business, friends), otherwise it is better to serve your military service.
In my opinion, it is better to have a HK passport than a Taiwan one, simply because our passport has more visa free countries than the ROC passport has. Good examples are Western Europe, Canada and ANZ.
HK has no right to question whether you have fulfilled your Taiwanese military obligation. Only Taiwan authorities can question and act upon that.