I can answer from the travel industry perspective @anon24369109 can probably answer from a real life perspective.
Airlines don’t care what travel documents you have as long as you can enter your destination legally. If you have 2 passports/travel documents whichever one you didn’t enter when you booked will probably be added when you checked in.
Permanent residents have basically the same rights in Australia as NWOHR do in Taiwan… except for travel documents.
Me. 
Exempt in the US.
Uses eVisitor for Australia
… ETA ?
No. I use eVisitor. ETA is $20.
I have the choice
Gotcha
OK first. Some countries like USA and Australia if you are a citizen you must enter on your Australian or US passport you cannot enter on a foreign passport. I travel to Australia, I book using my Taiwan name and passport on China Airlines. My Chinese name being different from my Australian name. So to be able to board all I need is my Australian passport as I cannot have an Australian visa in my Taiwan passport. The fact that my passports have different name & nationality is not important. When I land in Australia I must use my Australian passport to enter. However immigration in Australia have also registered my Taiwan passport and when I leave I use my Taiwan passport as it matches my boarding pass name. I use my Taiwan Identity for Philippines but Australian passport to enter and leave.
If you are an ROC citizen but enter Taiwan on a foreign passport then you are treated as a foreigner. You lose your right to work etc and if I enter visa exempt must leave in 90 days.
Why would I though? Now of course some dual citizen younger males enter on foreign passport so they can leave without military service obligation. This also is not an issue.
Electronic Travel Authority.
All foreigners need a visa to enter Australia. No discrimination at all 
ETA is still a visa.
Sone some cases people can get a non citizen travel document when they are resident in Australia. Refugees, those that cannot get passports from home country etc.
Maybe you too
Thank you for all these details. I wish I could say I understood all of it (especially the obvious disconnect between who the airline thinks it is flying and who then shows up at Australian border control), but I can’t. Glad this works for you though! 
Guy
Italians are not eligible for ETA. Italians must use eVisitor. It’s free.
Damn you @marco with your fist full of passports 
!
Guy
Every post I make that talks about dual citizenship should be imagined it has parentheses saying triple citizenship for me.
Yes for EU citizens. Still a visa though
All the airlines needs to know is that you either have a visa or an Australian passport when flying to Australia. They confirm this at check in. They don’t care what passport or nationality you use to book the flight.
Oh I wasn’t denying that. Just saying I don’t have to use ETA.
For me, a free visa might as well be visa free.
Guess so. It’s free for me to enter Australia and EU too lol
Btw there’s no way Taiwan checks for multiple citizenship when naturalizing right? you only need to renounce one of those citizenships
No, they do not care. A friend I advised changed his ARC from NZ citizen to Canadian citizen and renounced his Canadian to get ROC citizenship. Only required to renounce one.
He is well known on FB groups. John Lamorie
It’s been like this since I naturalized in the 1990’s so has probably always been this way. I know several who have renounced having multiple citizenships in hand already. They also don’t care if you resume or get multiple other citizenships as some have done.
That would just show you know how to act like . . . (non-naturalized) Taiwanese, who love collecting those passports too.
Guy