I think times have changed, both societal and technological. 20 odd years ago when it was suggested, people believed that ALL their records would be held on the chip on the card, i.e. medical, criminal, etc. I don't recall politicians saying otherwise.
Now, all it needs is an ID card confirming the person's name, photo and date of birth (basically like the photo driving licence). It could contain a unique reference number (more likely a bar code), to identify them across all governmental databases. But data would not be held on the card chip itself, just the ID. So a police officer could scan the card to see the criminal record. A doctor could scan the card to see medical history. But only via their own access to their own relevant databases. A police officer couldn't see medical history because all they have access to is the police database etc.
Now we have the internet, mobile internet. and 5g rolling out, there's no longer a need for the data to be on the card, just an ID number for the "official" to access the relevant data using their own access credentials.
I think the public would be much more open to such a "modern" card in the knowledge that, say, a thief, couldn't hack their card to see all their data - all they could "hack" would be what was on the card anyway, i.e. name, photo, dob, just like a photo driving licence, or say a credit card.
Societal changes, especially the massive increase in lawlessness (not just rioting and serious crimes, but also the epidemic of low level crime such as shoplifting, anti social behaviour, public transport fare evasion etc), means generally law abiding people want more action against criminals, so would support better ways of the authorities identifying potential criminals.