That I don’t know. A birth certificate is a birth certificate and it will be very difficult to deny paternity, if it comes down to it.
It sounds like it might be one of those wait and see situations. Your wife might have to be the one who convinces her parents to come around on the topic, and this might be doable, once they see their grandchild. Even if they hate you and want nothing to do with you, it would be counter-cultural (as in a failure to live up to their familial duty) to deny their own blood something like that. She could frame it as “Your granddaughter will be a bastard in Taiwan if you insist on not helping.”
Or, if you haven’t approached the topic with her family, yet, maybe she should proceed as if nothing was wrong and have the housing authorities tell her family that the father must be registered, as well, or the baby won’t have a legitimate father listed. Taiwanese people hate embarrassment and they might just go along with it to avoid an awkward situation at the housing office.
Of course, I don’t know your actual situation, so I’ll leave you to take those ideas for whatever they’re worth. I do think there is not much point in worrying about it now, as there is truly nothing anyone can do before the fact. See how it plays out once they have the baby in their arms.
Heads up on one point, though. If you don’t live in Taiwan, your daughter’s ID will lose validity after two years. It doesn’t mean that she will lose her nationality, but if she ever did want to go back to Taiwan, she would have to re-register herself again (unless she was back often enough to keep it valid). The same goes for the insurance (I don’t know how long that stays valid), which must be paid monthly (it’s not a lot of money). She can definitely get into the system, but her account will need to be maintained, even if she’s not there.